% Mizar problem: e2_17_1,fraenkel,392,32 
include('Axioms/SET010^1.ax').
thf(f1_s14_fraenkel_type,type,( f1_s14_fraenkel: $i )).
thf(f2_s14_fraenkel_type,type,( f2_s14_fraenkel: $i > $i )).
thf(m1_subset_1_type,type,( m1_subset_1: $i > $i > $o )).
thf(p1_s14_fraenkel_type,type,( p1_s14_fraenkel: $i > $o )).
thf(p2_s14_fraenkel_type,type,( p2_s14_fraenkel: $i > $o )).
thf(antisymmetry_r2_hidden,axiom,( ! [A: $i] : ! [B: $i] : ( ( r2_hidden @ A @ B ) => ~ ( r2_hidden @ B @ A ) ) ),file(hidden,r2_hidden)).
thf(dt_m1_subset_1,axiom,( $true ),file(subset_1,m1_subset_1)).
thf(dt_f1_s14_fraenkel,axiom,( $true ),file(fraenkel,f1_s14_fraenkel)).
thf(dt_f2_s14_fraenkel,axiom,( $true ),file(fraenkel,f2_s14_fraenkel)).
thf(e1_17_1__fraenkel,axiom,( ! [A: $i] : ( ( m1_subset_1 @ A @ f1_s14_fraenkel ) => ( ( ( r2_hidden @ A @ ( replSep1 @ ^ [B: $i] : ( m1_subset_1 @ B @ f1_s14_fraenkel ) @ ^ [B: $i] : B @ ^ [B: $i] : ( p2_s14_fraenkel @ B ) ) ) & ( p1_s14_fraenkel @ A ) ) <=> ( ( p2_s14_fraenkel @ A ) & ( p1_s14_fraenkel @ A ) ) ) ) ),file(fraenkel,e1_17_1__fraenkel)).
thf(s3_fraenkel,axiom,( ! [A: $i > $i] : ! [B: $i > $o] : ! [C: $i > $o] : ! [D: $i] : ( ! [E: $i] : ( ( m1_subset_1 @ E @ D ) => ( ( C @ E ) <=> ( B @ E ) ) ) => ( = @ ( replSep1 @ ^ [E: $i] : ( m1_subset_1 @ E @ D ) @ ^ [E: $i] : ( A @ E ) @ ^ [E: $i] : ( C @ E ) ) @ ( replSep1 @ ^ [E: $i] : ( m1_subset_1 @ E @ D ) @ ^ [E: $i] : ( A @ E ) @ ^ [E: $i] : ( B @ E ) ) ) ) ),file(fraenkel,s3_fraenkel)).
thf(e2_17_1__fraenkel,conjecture,( = @ ( replSep1 @ ^ [A: $i] : ( m1_subset_1 @ A @ f1_s14_fraenkel ) @ ^ [A: $i] : ( f2_s14_fraenkel @ A ) @ ^ [A: $i] : ( ( r2_hidden @ A @ ( replSep1 @ ^ [B: $i] : ( m1_subset_1 @ B @ f1_s14_fraenkel ) @ ^ [B: $i] : B @ ^ [B: $i] : ( p2_s14_fraenkel @ B ) ) ) & ( p1_s14_fraenkel @ A ) ) ) @ ( replSep1 @ ^ [A: $i] : ( m1_subset_1 @ A @ f1_s14_fraenkel ) @ ^ [A: $i] : ( f2_s14_fraenkel @ A ) @ ^ [A: $i] : ( ( p2_s14_fraenkel @ A ) & ( p1_s14_fraenkel @ A ) ) ) ),file(fraenkel,e2_17_1__fraenkel)).
thf(sethood_m1_subset_1,axiom,( ! [A: $i] : ( sethood @ ^ [X: $i] : ( m1_subset_1 @ X @ A ) ) ),file(subset_1,m1_subset_1)).
