Theorem imdistanri 672

Description: Distribution of implication with conjunction. (Contributed by NM, 8-Jan-2002.)

Hypothesis

Ref	Expression
imdistanri.1	|- (ph -> (ps -> ch))

Assertion

Ref	Expression
imdistanri	|- ((ps /\ ph) -> (ch /\ ph))

Proof of Theorem imdistanri

Step	Hyp	Ref	Expression
1		imdistanri.1	. . 3 |- (ph -> (ps -> ch))
2	1	com12 27	. 2 |- (ps -> (ph -> ch))
3	2	impac 604	1 |- ((ps /\ ph) -> (ch /\ ph))

This proof depends on syntax axioms:   -> wi 4   /\ wa 358

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 177  df-an 360

This theorem is used by: (None)