Theorem bj-aecomsv

Description: Version of aecoms with a disjoint variable condition, provable from Tarski's FOL. The corresponding version of naecoms should not be very useful since -. A. x x = y , DV ( x , y ) is true when the universe has at least two objects (see dtru ). (Contributed by BJ, 31-May-2019) (Proof modification is discouraged.)

	Ref	Expression
Hypothesis	bj-aecomsv.1	$$⊢\forall xx=y\to \phi$$
Assertion	bj-aecomsv	$$⊢\forall yy=x\to \phi$$

Proof

Step	Hyp	Ref	Expression
1		bj-aecomsv.1	$$⊢\forall xx=y\to \phi$$
2		aevlem	$$⊢\forall yy=x\to \forall xx=y$$
3	2 1	syl	$$⊢\forall yy=x\to \phi$$