Theorem 3jaodan 890

Description: Disjunction of 3 antecedents (deduction).

Hypotheses

Ref	Expression
3jaodan.1	|- ((ph /\ ps) -> ch)
3jaodan.2	|- ((ph /\ th) -> ch)
3jaodan.3	|- ((ph /\ ta) -> ch)

Assertion

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

Proof of Theorem 3jaodan

Step	Hyp	Ref	Expression
1		3jaodan.1	. . . 4 |- ((ph /\ ps) -> ch)
2	1	ex 373	. . 3 |- (ph -> (ps -> ch))
3		3jaodan.2	. . . 4 |- ((ph /\ th) -> ch)
4	3	ex 373	. . 3 |- (ph -> (th -> ch))
5		3jaodan.3	. . . 4 |- ((ph /\ ta) -> ch)
6	5	ex 373	. . 3 |- (ph -> (ta -> ch))
7	2, 4, 6	3jaod 888	. 2 |- (ph -> ((ps \/ th \/ ta) -> ch))
8	7	imp 350	1 |- ((ph /\ (ps \/ th \/ ta)) -> ch)

Syntax hints:   -> wi 3   /\ wa 223   \/ w3o 774

This theorem is referenced by:  xrltnsymt 5550  xrlttrit 5552  xrlttrt 5553  xrub 6080  zeot 6199  qbtwnxr 6279  tgioolem 7914

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

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