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	$$⊢A=B\to \forall x\in Ax\in B$$

Proof

Step	Hyp	Ref	Expression
1		ralel	$$⊢\forall x\in Bx\in B$$
2		id	$$⊢A=B\to A=B$$
3	2	raleqdv	$$⊢A=B\to \left(\forall x\in Ax\in B\leftrightarrow \forall x\in Bx\in B\right)$$
4	1 3	mpbiri	$$⊢A=B\to \forall x\in Ax\in B$$