Theorem 3jaoian 1247

Description: Disjunction of 3 antecedents (inference). (Contributed by NM, 14-Oct-2005.)

Hypotheses

Ref	Expression
3jaoian.1	|- ((ph /\ ps) -> ch)
3jaoian.2	|- ((th /\ ps) -> ch)
3jaoian.3	|- ((ta /\ ps) -> ch)

Assertion

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

Proof of Theorem 3jaoian

Step	Hyp	Ref	Expression
1		3jaoian.1	. . . 4 |- ((ph /\ ps) -> ch)
2	1	ex 423	. . 3 |- (ph -> (ps -> ch))
3		3jaoian.2	. . . 4 |- ((th /\ ps) -> ch)
4	3	ex 423	. . 3 |- (th -> (ps -> ch))
5		3jaoian.3	. . . 4 |- ((ta /\ ps) -> ch)
6	5	ex 423	. . 3 |- (ta -> (ps -> ch))
7	2, 4, 6	3jaoi 1245	. 2 |- ((ph \/ th \/ ta) -> (ps -> ch))
8	7	imp 418	1 |- (((ph \/ th \/ ta) /\ ps) -> ch)

Syntax hints:   -> wi 4   /\ wa 358   \/ w3o 933

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: (None)