Theorem mp2ani 714

Description: An inference based on modus ponens. (Contributed by NM, 12-Dec-2004.)

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 712	. 2 |- ( ph -> ( ch -> th ) )
5	1, 4	mpi 20	1 |- ( ph -> th )

Syntax hints:   -> wi 4   /\ wa 384

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 197  df-an 386

This theorem is referenced by:  dfom3  8544  dfac5lem4  8949  dfac9  8958  cflem  9068  canthp1lem2  9475  addsrpr  9896  mulsrpr  9897  trclublem  13734  gcdaddmlem  15245  sto1i  29095  stji1i  29101  kur14lem9  31196  dfon2lem4  31691  rtrclex  37924  comptiunov2i  37998