Theorem raleleqALT

Description: Alternate proof of raleleq using ralel , being longer and using more axioms. (Contributed by AV, 30-Oct-2020) (New usage is discouraged.) (Proof modification is discouraged.)

	Ref	Expression
Assertion	raleleqALT	|- ( A = B -> A. x e. A x e. B )

Proof

Step	Hyp	Ref	Expression
1		ralel	|- A. x e. B x e. B
2		id	|- ( A = B -> A = B )
3	2	raleqdv	|- ( A = B -> ( A. x e. A x e. B <-> A. x e. B x e. B ) )
4	1 3	mpbiri	|- ( A = B -> A. x e. A x e. B )