let p, q be Element of CQC-WFF ; :: thesis: ( p => q in TAUT iff ('not' ('not' p)) => q in TAUT )
thus ( p => q in TAUT implies ('not' ('not' p)) => q in TAUT ) :: thesis: ( ('not' ('not' p)) => q in TAUT implies p => q in TAUT )

proof

assume A1: p => q in TAUT ; :: thesis: ('not' ('not' p)) => q in TAUT
(p => q) => (('not' ('not' p)) => q) in TAUT by Th28;
hence ('not' ('not' p)) => q in TAUT by A1, CQC_THE1:46; :: thesis: verum

end;

assume A2: ('not' ('not' p)) => q in TAUT ; :: thesis: p => q in TAUT
(('not' ('not' p)) => q) => (p => q) in TAUT by Th28;
hence p => q in TAUT by A2, CQC_THE1:46; :: thesis: verum