Theorem bj-elequ12

Description: An identity law for the non-logical predicate, which combines elequ1 and elequ2 . For the analogous theorems for class terms, see eleq1 , eleq2 and eleq12 . TODO: move to main part. (Contributed by BJ, 29-Sep-2019)

	Ref	Expression
Assertion	bj-elequ12	|- ( ( x = y /\ z = t ) -> ( x e. z <-> y e. t ) )

Proof

Step	Hyp	Ref	Expression
1		elequ1	|- ( x = y -> ( x e. z <-> y e. z ) )
2		elequ2	|- ( z = t -> ( y e. z <-> y e. t ) )
3	1 2	sylan9bb	|- ( ( x = y /\ z = t ) -> ( x e. z <-> y e. t ) )