Theorem mp2ani 659

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 657	. 2 |- (ph -> (ch -> th))
5	1, 4	mpi 16	1 |- (ph -> th)

This proof depends on syntax axioms:   -> wi 4   /\ wa 358

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 177  df-an 360

This theorem is used by: (None)