Theorem imdistanri 446

Description: Distribution of implication with conjunction.

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 11	. 2 |- (ps -> (ph -> ch))
3	2	impac 389	1 |- ((ps /\ ph) -> (ch /\ ph))

Syntax hints:   -> wi 3   /\ wa 223

This theorem is referenced by:  pm5.61 449

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7

This theorem depends on definitions:  df-bi 147  df-an 225

Copyright terms: Public domain