Theorem 19.9d2r

Description: A deduction version of one direction of 19.9 with two variables. (Contributed by Thierry Arnoux, 30-Jan-2017)

	Ref	Expression
Hypotheses	19.9d2r.1	|- ( ph -> F/ x ps )
	19.9d2r.2	|- ( ph -> F/ y ps )
	19.9d2r.3	|- ( ph -> E. x e. A E. y e. B ps )
Assertion	19.9d2r	|- ( ph -> ps )

Proof

Step	Hyp	Ref	Expression
1		19.9d2r.1	|- ( ph -> F/ x ps )
2		19.9d2r.2	|- ( ph -> F/ y ps )
3		19.9d2r.3	|- ( ph -> E. x e. A E. y e. B ps )
4		nfv	|- F/ y ph
5	4 1 2 3	19.9d2rf	|- ( ph -> ps )