Theorem 3ori 1290

Description: Infer implication from triple disjunction. (Contributed by NM, 26-Sep-2006.)

Hypothesis

Ref	Expression
3ori.1	|- ( ph \/ ps \/ ch )

Assertion

Ref	Expression
3ori	|- ( ( -. ph /\ -. ps ) -> ch )

Proof of Theorem 3ori

Step	Hyp	Ref	Expression
1		ioran 742	. 2 |- ( -. ( ph \/ ps ) <-> ( -. ph /\ -. ps ) )
2		3ori.1	. . . 4 |- ( ph \/ ps \/ ch )
3		df-3or 969	. . . 4 |- ( ( ph \/ ps \/ ch ) <-> ( ( ph \/ ps ) \/ ch ) )
4	2, 3	mpbi 144	. . 3 |- ( ( ph \/ ps ) \/ ch )
5	4	ori 713	. 2 |- ( -. ( ph \/ ps ) -> ch )
6	1, 5	sylbir 134	1 |- ( ( -. ph /\ -. ps ) -> ch )

Syntax hints:   -. wn 3   -> wi 4   /\ wa 103   \/ wo 698   \/ w3o 967

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 604  ax-in2 605  ax-io 699

This theorem depends on definitions:  df-bi 116  df-3or 969

This theorem is referenced by: (None)