Theorem 3jaod 1246

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

Hypotheses

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

Assertion

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

Proof of Theorem 3jaod

Step	Hyp	Ref	Expression
1		3jaod.1	. 2 |- (ph -> (ps -> ch))
2		3jaod.2	. 2 |- (ph -> (th -> ch))
3		3jaod.3	. 2 |- (ph -> (ta -> ch))
4		3jao 1243	. 2 |- (((ps -> ch) /\ (th -> ch) /\ (ta -> ch)) -> ((ps \/ th \/ ta) -> ch))
5	1, 2, 3, 4	syl3anc 1182	1 |- (ph -> ((ps \/ th \/ ta) -> ch))

Syntax hints:   -> wi 4   \/ 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:  3jaodan  1248  3jaao  1249  ltfintri  4467  nchoicelem1  6290  nchoicelem2  6291