Theorem biimpac 326

Description: Inference from a logical equivalence.

Hypothesis

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

Assertion

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

Proof of Theorem biimpac

Step	Hyp	Ref	Expression
1		biimpa.1	. . 3 |- (ph -> (ps <-> ch))
2	1	biimpcd 137	. 2 |- (ps -> (ph -> ch))
3	2	imp 277	1 |- ((ps /\ ph) -> ch)

Syntax hints:   -> wi 2   <-> wb 127   /\ wa 196

This theorem is referenced by:  ordnbtwn 2316  f1oco 2816  xpmapenlem4 3394  aceq5lem4 3561  aceq5 3563  ltrpq 3879  map2psrpr 4014  addge0 4324  spansncv 5542  pjnormss 5638  sumdmdlem 5786

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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