Theorem mpanlr1 709

Description: An inference based on modus ponens.

Hypotheses

Ref	Expression
mpanlr1.1	|- ps
mpanlr1.2	|- (((ph /\ (ps /\ ch)) /\ th) -> ta)

Assertion

Ref	Expression
mpanlr1	|- (((ph /\ ch) /\ th) -> ta)

Proof of Theorem mpanlr1

Step	Hyp	Ref	Expression
1		mpanlr1.1	. . 3 |- ps
2		mpanlr1.2	. . . 4 |- (((ph /\ (ps /\ ch)) /\ th) -> ta)
3	2	ex 373	. . 3 |- ((ph /\ (ps /\ ch)) -> (th -> ta))
4	1, 3	mpanr1 707	. 2 |- ((ph /\ ch) -> (th -> ta))
5	4	imp 350	1 |- (((ph /\ ch) /\ th) -> ta)

Syntax hints:   -> wi 3   /\ wa 223

This theorem is referenced by:  oecl 4156  omass 4195  oen0 4197  oeordi 4198  oewordri 4203  oeworde 4204

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-an 225

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