% Mizar problem: e2_3_1,fraenkel,80,18 
include('Axioms/SET010^1.ax').
thf(f1_s3_fraenkel_type,type,( f1_s3_fraenkel: $i )).
thf(f2_s3_fraenkel_type,type,( f2_s3_fraenkel: $i > $i )).
thf(m1_subset_1_type,type,( m1_subset_1: $i > $i > $o )).
thf(p1_s3_fraenkel_type,type,( p1_s3_fraenkel: $i > $o )).
thf(p2_s3_fraenkel_type,type,( p2_s3_fraenkel: $i > $o )).
thf(r1_tarski_type,type,( r1_tarski: $i > $i > $o )).
thf(reflexivity_r1_tarski,axiom,( ! [A: $i] : ! [B: $i] : ( r1_tarski @ A @ A ) ),file(tarski,r1_tarski)).
thf(dt_m1_subset_1,axiom,( $true ),file(subset_1,m1_subset_1)).
thf(dt_f1_s3_fraenkel,axiom,( $true ),file(fraenkel,f1_s3_fraenkel)).
thf(dt_f2_s3_fraenkel,axiom,( $true ),file(fraenkel,f2_s3_fraenkel)).
thf(e1_3_1__fraenkel,axiom,( ! [A: $i] : ( ( m1_subset_1 @ A @ f1_s3_fraenkel ) => ( ( p1_s3_fraenkel @ A ) => ( p2_s3_fraenkel @ A ) ) ) ),file(fraenkel,e1_3_1__fraenkel)).
thf(s1_fraenkel,axiom,( ! [A: $i > $i] : ! [B: $i > $o] : ! [C: $i > $o] : ! [D: $i] : ( ! [E: $i] : ( ( m1_subset_1 @ E @ D ) => ( ( C @ E ) => ( B @ E ) ) ) => ( r1_tarski @ ( 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,s1_fraenkel)).
thf(e2_3_1__fraenkel,conjecture,( r1_tarski @ ( replSep1 @ ^ [A: $i] : ( m1_subset_1 @ A @ f1_s3_fraenkel ) @ ^ [A: $i] : ( f2_s3_fraenkel @ A ) @ ^ [A: $i] : ( p1_s3_fraenkel @ A ) ) @ ( replSep1 @ ^ [A: $i] : ( m1_subset_1 @ A @ f1_s3_fraenkel ) @ ^ [A: $i] : ( f2_s3_fraenkel @ A ) @ ^ [A: $i] : ( p2_s3_fraenkel @ A ) ) ),file(fraenkel,e2_3_1__fraenkel)).
thf(sethood_m1_subset_1,axiom,( ! [A: $i] : ( sethood @ ^ [X: $i] : ( m1_subset_1 @ X @ A ) ) ),file(subset_1,m1_subset_1)).
