let Y be non empty set ; :: thesis: for a, b being Function of Y,BOOLEAN holds a 'eqv' b = (a 'or' ('not' b)) '&' (('not' a) 'or' b)
let a, b be Function of Y,BOOLEAN; :: thesis: a 'eqv' b = (a 'or' ('not' b)) '&' (('not' a) 'or' b)
let x be Element of Y; :: according to FUNCT_2:def 8 :: thesis: K11((a 'eqv' b),x) = K11(((a 'or' ('not' b)) '&' (('not' a) 'or' b)),x)
((a 'or' ('not' b)) '&' (('not' a) 'or' b)) . x = ((a 'or' ('not' b)) '&' (a 'imp' b)) . x by BVFUNC_4:8
.= ((a 'imp' b) '&' (b 'imp' a)) . x by BVFUNC_4:8
.= (a 'eqv' b) . x by BVFUNC_4:7 ;
hence K11((a 'eqv' b),x) = K11(((a 'or' ('not' b)) '&' (('not' a) 'or' b)),x) ; :: thesis: verum