Theorem 3ori 1311

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 753	. 2 |- ( -. ( ph \/ ps ) <-> ( -. ph /\ -. ps ) )
2		3ori.1	. . . 4 |- ( ph \/ ps \/ ch )
3		df-3or 981	. . . 4 |- ( ( ph \/ ps \/ ch ) <-> ( ( ph \/ ps ) \/ ch ) )
4	2, 3	mpbi 145	. . 3 |- ( ( ph \/ ps ) \/ ch )
5	4	ori 724	. 2 |- ( -. ( ph \/ ps ) -> ch )
6	1, 5	sylbir 135	1 |- ( ( -. ph /\ -. ps ) -> ch )

Syntax hints:   -. wn 3   -> wi 4   /\ wa 104   \/ wo 709   \/ w3o 979

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-in1 615  ax-in2 616  ax-io 710

This theorem depends on definitions:  df-bi 117  df-3or 981

This theorem is referenced by: (None)