Theorem ancl 569

Description: Conjoin antecedent to left of consequent. (Contributed by NM, 15-Aug-1994.)

Assertion

Ref	Expression
ancl	|- ( ( ph -> ps ) -> ( ph -> ( ph /\ ps ) ) )

Proof of Theorem ancl

Step	Hyp	Ref	Expression
1		pm3.2 463	. 2 |- ( ph -> ( ps -> ( ph /\ ps ) ) )
2	1	a2i 14	1 |- ( ( ph -> ps ) -> ( ph -> ( ph /\ ps ) ) )

Syntax hints:   -> wi 4   /\ wa 384

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 197  df-an 386

This theorem is referenced by:  bnj1118  31052  bnj1128  31058  bnj1145  31061  bnj1174  31071