Theorem 3jaoi 1239

Description: Disjunction of 3 antecedents (inference). (Contributed by NM, 12-Sep-1995.)

Hypotheses

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

Assertion

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

Proof of Theorem 3jaoi

Step	Hyp	Ref	Expression
1		3jaoi.1	. . 3 |- ( ph -> ps )
2		3jaoi.2	. . 3 |- ( ch -> ps )
3		3jaoi.3	. . 3 |- ( th -> ps )
4	1, 2, 3	3pm3.2i 1121	. 2 |- ( ( ph -> ps ) /\ ( ch -> ps ) /\ ( th -> ps ) )
5		3jao 1237	. 2 |- ( ( ( ph -> ps ) /\ ( ch -> ps ) /\ ( th -> ps ) ) -> ( ( ph \/ ch \/ th ) -> ps ) )
6	4, 5	ax-mp 7	1 |- ( ( ph \/ ch \/ th ) -> ps )

Syntax hints:   -> wi 4   \/ w3o 923   /\ w3a 924

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 665

This theorem depends on definitions:  df-bi 115  df-3or 925  df-3an 926

This theorem is referenced by:  3jaoian  1241  3ianorr  1245  acexmidlem1  5648  nndceq  6260  nndcel  6261  znegcl  8779  xrltnr  9248  nltpnft  9277  ngtmnft  9278  xrrebnd  9279  xnegcl  9292  xnegneg  9293  xltnegi  9295