Theorem a5i 1592

Description: Inference generalizing a consequent. (Contributed by NM, 5-Aug-1993.)

Hypothesis

Ref	Expression
a5i.1	|- ( A. x ph -> ps )

Assertion

Ref	Expression
a5i	|- ( A. x ph -> A. x ps )

Proof of Theorem a5i

Step	Hyp	Ref	Expression
1		hba1 1589	. . 3 |- ( A. x ph -> A. x A. x ph )
2		ax-5 1496	. . 3 |- ( A. x ( A. x ph -> ps ) -> ( A. x A. x ph -> A. x ps ) )
3	1, 2	syl5 32	. 2 |- ( A. x ( A. x ph -> ps ) -> ( A. x ph -> A. x ps ) )
4		a5i.1	. 2 |- ( A. x ph -> ps )
5	3, 4	mpg 1500	1 |- ( A. x ph -> A. x ps )

Syntax hints:   -> wi 4   A.wal 1396

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-5 1496  ax-gen 1498  ax-ial 1583

This theorem is referenced by:  hbae  1766  equveli  1808  hbsb2a  1855  hbsb2e  1856  aev  1861  dveeq2or  1865  hbsb2  1885  nfsb2or  1886  reu6  3008