Theorem hbia1 1444

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 1433	. 2 |- ( A. x ph -> A. x A. x ph )
2		hba1 1433	. 2 |- ( A. x ps -> A. x A. x ps )
3	1, 2	hbim 1437	1 |- ( ( A. x ph -> A. x ps ) -> A. x ( A. x ph -> A. x ps ) )

Syntax hints:   -> wi 4   A.wal 1241

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-5 1336  ax-gen 1338  ax-4 1400  ax-ial 1427  ax-i5r 1428

This theorem is referenced by: (None)