Theorem imdistanri 341

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 13	. 2 |- (ps -> (ph -> ch))
3	2	impac 304	1 |- ((ps /\ ph) -> (ch /\ ph))

Syntax hints:   -> wi 2   /\ wa 196

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

This theorem depends on definitions:  df-bi 128  df-an 198

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