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

q => (s => p) in TAUT A

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

assume A1: s => (q => p) in TAUT A ; :: thesis: q => (s => p) in TAUT A

(s => (q => p)) => (q => (s => p)) in TAUT A by Th8;

hence q => (s => p) in TAUT A by A1, CQC_THE1:46; :: thesis: verum

q => (s => p) in TAUT A

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

assume A1: s => (q => p) in TAUT A ; :: thesis: q => (s => p) in TAUT A

(s => (q => p)) => (q => (s => p)) in TAUT A by Th8;

hence q => (s => p) in TAUT A by A1, CQC_THE1:46; :: thesis: verum