Theorem mp2ani 699

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 697	. 2 |- (ph -> (ch -> th))
5	1, 4	mpi 44	1 |- (ph -> th)

Syntax hints:   -> wi 3   /\ wa 223

This theorem is referenced by:  csbie2t 2029  th3q 4307  dfom3 4610  aceq5lem4 4718  cflem 4885  mulc1cncf 7222  pjcomp 9559  sto1 10101  stji1 10107  abfi 10385

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

Copyright terms: Public domain