let A be QC-alphabet ; :: thesis: for p, q being Element of CQC-WFF A holds
( ( p => q is valid & q => p is valid ) iff p <=> q is valid )
let p, q be Element of CQC-WFF A; :: thesis: ( ( p => q is valid & q => p is valid ) iff p <=> q is valid )
thus ( p => q is valid & q => p is valid implies p <=> q is valid ) :: thesis: ( p <=> q is valid implies ( p => q is valid & q => p is valid ) )

proof

assume ( p => q is valid & q => p is valid ) ; :: thesis: p <=> q is valid
then (p => q) '&' (q => p) is valid by Lm8;
hence p <=> q is valid by QC_LANG2:def 4; :: thesis: verum

end;

assume p <=> q is valid ; :: thesis: ( p => q is valid & q => p is valid )
then (p => q) '&' (q => p) is valid by QC_LANG2:def 4;
hence ( p => q is valid & q => p is valid ) by Lm2; :: thesis: verum