Theorem 3jaoi 1245

Description: Disjunction of 3 antecedents (inference). (Contributed by NM, 12-Sep-1995.)

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 1130	. 2 |- ((ph -> ps) /\ (ch -> ps) /\ (th -> ps))
5		3jao 1243	. 2 |- (((ph -> ps) /\ (ch -> ps) /\ (th -> ps)) -> ((ph \/ ch \/ th) -> ps))
6	4, 5	ax-mp 5	1 |- ((ph \/ ch \/ th) -> ps)

Syntax hints:   -> wi 4   \/ w3o 933   /\ w3a 934

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3or 935  df-3an 936

This theorem is referenced by:  3jaoian  1247