Theorem 3jaoi 887

Description: Disjunction of 3 antecedents (inference).

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 818	. 2 |- ((ph -> ps) /\ (ch -> ps) /\ (th -> ps))
5		3jao 886	. 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 3   \/ w3o 774   /\ w3a 775

This theorem is referenced by:  3jaoian 889  ordzsl 3116  oawordeulem 4188  r1val1 4658  rankr1 4674  xrltnrt 5541  xrsupsslem 6076  xrinfmsslem 6077  znegclt 6163

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

Copyright terms: Public domain