Theorem 3jaoian 1346

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

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 115	. . 3 |- ( ph -> ( ps -> ch ) )
3		3jaoian.2	. . . 4 |- ( ( th /\ ps ) -> ch )
4	3	ex 115	. . 3 |- ( th -> ( ps -> ch ) )
5		3jaoian.3	. . . 4 |- ( ( ta /\ ps ) -> ch )
6	5	ex 115	. . 3 |- ( ta -> ( ps -> ch ) )
7	2, 4, 6	3jaoi 1344	. 2 |- ( ( ph \/ th \/ ta ) -> ( ps -> ch ) )
8	7	imp 124	1 |- ( ( ( ph \/ th \/ ta ) /\ ps ) -> ch )

This proof depends on syntax axioms:   -> wi 4   /\ wa 104   \/ w3o 1008

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 721

This proof depends on definitions:  df-bi 117  df-3or 1010  df-3an 1011

This theorem is used by:  xrltnsym  10195  xrlttr  10197  xltnegi  10237  xaddcom  10263  xnegdi  10270  qbtwnxr  10692