Theorem equs4v

Description: Version of equs4 with a disjoint variable condition, which requires fewer axioms. (Contributed by NM, 10-May-1993) (Revised by BJ, 31-May-2019)

	Ref	Expression
Assertion	equs4v	|- ( A. x ( x = y -> ph ) -> E. x ( x = y /\ ph ) )

Proof

Step	Hyp	Ref	Expression
1		ax6ev	|- E. x x = y
2		exintr	|- ( A. x ( x = y -> ph ) -> ( E. x x = y -> E. x ( x = y /\ ph ) ) )
3	1 2	mpi	|- ( A. x ( x = y -> ph ) -> E. x ( x = y /\ ph ) )