let A be QC-alphabet ; :: thesis: for p, q being Element of CQC-WFF A st q in TAUT A holds

p => q in TAUT A

let p, q be Element of CQC-WFF A; :: thesis: ( q in TAUT A implies p => q in TAUT A )

q => (p => q) in TAUT A by Th5;

hence ( q in TAUT A implies p => q in TAUT A ) by CQC_THE1:46; :: thesis: verum

p => q in TAUT A

let p, q be Element of CQC-WFF A; :: thesis: ( q in TAUT A implies p => q in TAUT A )

q => (p => q) in TAUT A by Th5;

hence ( q in TAUT A implies p => q in TAUT A ) by CQC_THE1:46; :: thesis: verum