Theorem 3jaod 888

Description: Disjunction of 3 antecedents (deduction).

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		3jao 886	. 2 |- (((ps -> ch) /\ (th -> ch) /\ (ta -> ch)) -> ((ps \/ th \/ ta) -> ch))
2		3jaod.1	. 2 |- (ph -> (ps -> ch))
3		3jaod.2	. 2 |- (ph -> (th -> ch))
4		3jaod.3	. 2 |- (ph -> (ta -> ch))
5	1, 2, 3, 4	syl3anc 858	1 |- (ph -> ((ps \/ th \/ ta) -> ch))

Syntax hints:   -> wi 3   \/ w3o 774

This theorem is referenced by:  3jaodan 890  xrsupsslem 6076  xrinfmsslem 6077  xrub 6080  supxrre 6083

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 776  df-3an 777

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