Theorem 3ori 1157

Description: Infer implication from triple disjunction.

Hypothesis

Ref	Expression
3ori.1	|- (ph \/ ps \/ ch)

Assertion

Ref	Expression
3ori	|- ((-. ph /\ -. ps) -> ch)

Proof of Theorem 3ori

Step	Hyp	Ref	Expression
1		ioran 331	. 2 |- (-. (ph \/ ps) <-> (-. ph /\ -. ps))
2		3ori.1	. . . 4 |- (ph \/ ps \/ ch)
3		df-3or 859	. . . 4 |- ((ph \/ ps \/ ch) <-> ((ph \/ ps) \/ ch))
4	2, 3	mpbi 206	. . 3 |- ((ph \/ ps) \/ ch)
5	4	ori 247	. 2 |- (-. (ph \/ ps) -> ch)
6	1, 5	sylbir 218	1 |- ((-. ph /\ -. ps) -> ch)

Syntax hints:  -. wn 2   -> wi 3   \/ wo 239   /\ wa 240   \/ w3o 857

This theorem is referenced by:  rankxplim3 5825

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 164  df-or 241  df-an 242  df-3or 859

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