Theorem orcanai 689

Description: Change disjunction in consequent to conjunction in antecedent.

Hypothesis

Ref	Expression
orcanai.1	|- (ph -> (ps \/ ch))

Assertion

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

Proof of Theorem orcanai

Step	Hyp	Ref	Expression
1		orcanai.1	. . 3 |- (ph -> (ps \/ ch))
2	1	ord 232	. 2 |- (ph -> (-. ps -> ch))
3	2	imp 350	1 |- ((ph /\ -. ps) -> ch)

Syntax hints:  -. wn 2   -> wi 3   \/ wo 222   /\ wa 223

This theorem is referenced by:  dflim3 3113  bren2 4376  php 4499  xrmax2 5866  xrmin1 5867  dscmet 7870

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-or 224  df-an 225

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