let Al be QC-alphabet ; :: thesis: for p being Element of CQC-WFF Al
for A being non empty set
for J being interpretation of Al,A
for v being Element of Valuations_in (Al,A)
for Sub being CQC_Substitution of Al holds
( J,v |= [p,Sub] iff J,v |= p )
let p be Element of CQC-WFF Al; :: thesis: for A being non empty set
for J being interpretation of Al,A
for v being Element of Valuations_in (Al,A)
for Sub being CQC_Substitution of Al holds
( J,v |= [p,Sub] iff J,v |= p )
let A be non empty set ; :: thesis: for J being interpretation of Al,A
for v being Element of Valuations_in (Al,A)
for Sub being CQC_Substitution of Al holds
( J,v |= [p,Sub] iff J,v |= p )
let J be interpretation of Al,A; :: thesis: for v being Element of Valuations_in (Al,A)
for Sub being CQC_Substitution of Al holds
( J,v |= [p,Sub] iff J,v |= p )
let v be Element of Valuations_in (Al,A); :: thesis: for Sub being CQC_Substitution of Al holds
( J,v |= [p,Sub] iff J,v |= p )
let Sub be CQC_Substitution of Al; :: thesis: ( J,v |= [p,Sub] iff J,v |= p )
( J,v |= [p,Sub] iff J,v |= [p,Sub] `1 ) by SUBLEMMA:def 2;
hence ( J,v |= [p,Sub] iff J,v |= p ) ; :: thesis: verum