% Mizar problem: e3_61_2_2,ordinal1,1310,19 
include('Axioms/SET010^0.ax').
thf(c1_61_type,type,( c1_61__ordinal1: $i )).
thf(c1_61_2_2_type,type,( c1_61_2_2__ordinal1: $i )).
thf(c2_61_2_2_type,type,( c2_61_2_2__ordinal1: $i )).
thf(v1_ordinal1_type,type,( v1_ordinal1: $i > $o )).
thf(v2_ordinal1_type,type,( v2_ordinal1: $i > $o )).
thf(v3_ordinal1_type,type,( v3_ordinal1: $i > $o )).
thf(v4_ordinal1_type,type,( v4_ordinal1: $i > $o )).
thf(cc2_ordinal1,axiom,( ! [A: $i] : ( ( ( v1_ordinal1 @ A ) & ( v2_ordinal1 @ A ) ) => ( v3_ordinal1 @ A ) ) ),file(ordinal1,cc2_ordinal1)).
thf(antisymmetry_r2_hidden,axiom,( ! [A: $i] : ! [B: $i] : ( ( r2_hidden @ A @ B ) => ~ ( r2_hidden @ B @ A ) ) ),file(hidden,r2_hidden)).
thf(dt_c1_61__ordinal1,axiom,( $true ),file(ordinal1,c1_61__ordinal1)).
thf(dt_c1_61_2_2__ordinal1,axiom,( $true ),file(ordinal1,c1_61_2_2__ordinal1)).
thf(dt_c2_61_2_2__ordinal1,axiom,( $true ),file(ordinal1,c2_61_2_2__ordinal1)).
thf(cc1_ordinal1,axiom,( ! [A: $i] : ( ( v3_ordinal1 @ A ) => ( ( v1_ordinal1 @ A ) & ( v2_ordinal1 @ A ) ) ) ),file(ordinal1,cc1_ordinal1)).
thf(rc1_ordinal1,axiom,( ? [A: $i] : ( v3_ordinal1 @ A ) ),file(ordinal1,rc1_ordinal1)).
thf(e1_61_2_2__ordinal1,axiom,( ! [A: $i] : ( ( r2_hidden @ A @ c1_61_2_2__ordinal1 ) <=> ( ( r2_hidden @ A @ c1_61__ordinal1 ) & ? [B: $i] : ( ( v3_ordinal1 @ B ) & ( = @ A @ B ) & ( v4_ordinal1 @ B ) ) ) ) ),file(ordinal1,e1_61_2_2__ordinal1)).
thf(e2_61_2_2__ordinal1,axiom,( ! [A: $i] : ( ( r2_hidden @ A @ c2_61_2_2__ordinal1 ) <=> ( ( r2_hidden @ A @ c1_61__ordinal1 ) & ? [B: $i] : ( ( v3_ordinal1 @ B ) & ( = @ A @ B ) & ( v4_ordinal1 @ B ) ) ) ) ),file(ordinal1,e2_61_2_2__ordinal1)).
thf(s2_xboole_0,axiom,( ! [A: $i] : ! [B: $i > $o] : ! [C: $i] : ( ( ! [D: $i] : ( ( r2_hidden @ D @ C ) <=> ( B @ D ) ) & ! [D: $i] : ( ( r2_hidden @ D @ A ) <=> ( B @ D ) ) ) => ( = @ C @ A ) ) ),file(xboole_0,s2_xboole_0)).
thf(e3_61_2_2__ordinal1,conjecture,( = @ c1_61_2_2__ordinal1 @ c2_61_2_2__ordinal1 ),file(ordinal1,e3_61_2_2__ordinal1)).
