let p be Element of CQC-WFF ; :: thesis: for A being non empty set
for J being interpretation of A
for v being Element of Valuations_in A
for Sub being CQC_Substitution holds
( J,v |= [p,Sub] iff J,v |= p )
let A be non empty set ; :: thesis: for J being interpretation of A
for v being Element of Valuations_in A
for Sub being CQC_Substitution holds
( J,v |= [p,Sub] iff J,v |= p )
let J be interpretation of A; :: thesis: for v being Element of Valuations_in A
for Sub being CQC_Substitution holds
( J,v |= [p,Sub] iff J,v |= p )
let v be Element of Valuations_in A; :: thesis: for Sub being CQC_Substitution holds
( J,v |= [p,Sub] iff J,v |= p )
let Sub be CQC_Substitution; :: 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 ) by MCART_1:7; :: thesis: verum