Theorem 3jaoi 633

Description: Disjunction of 3 antecedents (inference).

Hypotheses

Ref	Expression
3jaoi.1	|- (ph -> ps)
3jaoi.2	|- (ch -> ps)
3jaoi.3	|- (th -> ps)

Assertion

Ref	Expression
3jaoi	|- ((ph \/ ch \/ th) -> ps)

Proof of Theorem 3jaoi

Step	Hyp	Ref	Expression
1		3jaoi.1	. . 3 |- (ph -> ps)
2		3jaoi.2	. . 3 |- (ch -> ps)
3		3jaoi.3	. . 3 |- (th -> ps)
4	1, 2, 3	3pm3.2i 603	. 2 |- ((ph -> ps) /\ (ch -> ps) /\ (th -> ps))
5		3jao 632	. 2 |- (((ph -> ps) /\ (ch -> ps) /\ (th -> ps)) -> ((ph \/ ch \/ th) -> ps))
6	4, 5	ax-mp 6	1 |- ((ph \/ ch \/ th) -> ps)

Syntax hints:   -> wi 2   \/ w3o 580   /\ w3a 581

This theorem is referenced by:  ordzsl 2366  oawordeulem 3156  r1val1 3502  rankr1 3518  znegclt 4588

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-or 197  df-an 198  df-3or 582  df-3an 583

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