Theorem 3jaoian 886

Description: Disjunction of 3 antecedents (inference).

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 373	. . 3 |- (ph -> (ps -> ch))
3		3jaoian.2	. . . 4 |- ((th /\ ps) -> ch)
4	3	ex 373	. . 3 |- (th -> (ps -> ch))
5		3jaoian.3	. . . 4 |- ((ta /\ ps) -> ch)
6	5	ex 373	. . 3 |- (ta -> (ps -> ch))
7	2, 4, 6	3jaoi 884	. 2 |- ((ph \/ th \/ ta) -> (ps -> ch))
8	7	imp 350	1 |- (((ph \/ th \/ ta) /\ ps) -> ch)

Syntax hints:   -> wi 3   /\ wa 223   \/ w3o 772

This theorem is referenced by:  xrltnsymt 5523  xrlttrit 5525  xrlttrt 5526  qbtwnxr 6217  tgioolem 7853

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  df-3or 774  df-3an 775

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