Theorem hbia1 1566

Description: Lemma 23 of [Monk2] p. 114. (Contributed by NM, 29-May-2008.)

Assertion

Ref	Expression
hbia1	|- ( ( A. x ph -> A. x ps ) -> A. x ( A. x ph -> A. x ps ) )

Proof of Theorem hbia1

Step	Hyp	Ref	Expression
1		hba1 1554	. 2 |- ( A. x ph -> A. x A. x ph )
2		hba1 1554	. 2 |- ( A. x ps -> A. x A. x ps )
3	1, 2	hbim 1559	1 |- ( ( A. x ph -> A. x ps ) -> A. x ( A. x ph -> A. x ps ) )

Syntax hints:   -> wi 4   A.wal 1362

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-5 1461  ax-gen 1463  ax-4 1524  ax-ial 1548  ax-i5r 1549

This theorem is referenced by: (None)