Theorem 2stdpc5

Description: A double stdpc5 (one direction of PM*11.3). See also 2stdpc4 and 19.21vv . (Contributed by BJ, 15-Sep-2018) (Proof modification is discouraged.)

	Ref	Expression
Hypotheses	2stdpc5.1	|- F/ x ph
	2stdpc5.2	|- F/ y ph
Assertion	2stdpc5	|- ( A. x A. y ( ph -> ps ) -> ( ph -> A. x A. y ps ) )

Proof

Step	Hyp	Ref	Expression
1		2stdpc5.1	|- F/ x ph
2		2stdpc5.2	|- F/ y ph
3	2	stdpc5	|- ( A. y ( ph -> ps ) -> ( ph -> A. y ps ) )
4	3	alimi	|- ( A. x A. y ( ph -> ps ) -> A. x ( ph -> A. y ps ) )
5	1	stdpc5	|- ( A. x ( ph -> A. y ps ) -> ( ph -> A. x A. y ps ) )
6	4 5	syl	|- ( A. x A. y ( ph -> ps ) -> ( ph -> A. x A. y ps ) )