let A be QC-alphabet ; :: thesis: for p, q, r being Element of CQC-WFF A st r => p in TAUT A & r => q in TAUT A holds
r => (p '&' q) in TAUT A
let p, q, r be Element of CQC-WFF A; :: thesis: ( r => p in TAUT A & r => q in TAUT A implies r => (p '&' q) in TAUT A )
assume that
A1: r => p in TAUT A and
A2: r => q in TAUT A ; :: thesis: r => (p '&' q) in TAUT A
(r => p) => ((r => q) => (r => (p '&' q))) in TAUT A by Th33;
then (r => q) => (r => (p '&' q)) in TAUT A by A1, CQC_THE1:46;
hence r => (p '&' q) in TAUT A by A2, CQC_THE1:46; :: thesis: verum