let G1, G2, H1, H2 be ZF-formula; :: thesis: for x, y being Variable holds
( G1 <=> G2 = (H1 <=> H2) / (x,y) iff ( G1 = H1 / (x,y) & G2 = H2 / (x,y) ) )
let x, y be Variable; :: thesis: ( G1 <=> G2 = (H1 <=> H2) / (x,y) iff ( G1 = H1 / (x,y) & G2 = H2 / (x,y) ) )
( G1 <=> G2 = (H1 <=> H2) / (x,y) iff ( G1 => G2 = (H1 => H2) / (x,y) & G2 => G1 = (H2 => H1) / (x,y) ) ) by Th158;
hence ( G1 <=> G2 = (H1 <=> H2) / (x,y) iff ( G1 = H1 / (x,y) & G2 = H2 / (x,y) ) ) by Th162; :: thesis: verum