Theorem mp2ani 523

Description: An inference based on modus ponens.

Hypotheses

Ref	Expression
mp2ani.1	|- ps
mp2ani.2	|- ch
mp2ani.3	|- (ph -> ((ps /\ ch) -> th))

Assertion

Ref	Expression
mp2ani	|- (ph -> th)

Proof of Theorem mp2ani

Step	Hyp	Ref	Expression
1		mp2ani.2	. 2 |- ch
2		mp2ani.1	. . 3 |- ps
3		mp2ani.3	. . 3 |- (ph -> ((ps /\ ch) -> th))
4	2, 3	mpani 521	. 2 |- (ph -> (ch -> th))
5	1, 4	mpi 44	1 |- (ph -> th)

Syntax hints:   -> wi 2   /\ wa 196

This theorem is referenced by:  th3q 3253  dfom3 3477  aceq5lem4 3561  cflem 3700  pjcomp 5565  pjoi0 5592  sto1 5677  stji1 5683  stcltr1 5707

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6

This theorem depends on definitions:  df-bi 128  df-an 198

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