Theorem mp2ani 429

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 427	. 2 |- ( ph -> ( ch -> th ) )
5	1, 4	mpi 15	1 |- ( ph -> th )

Syntax hints:   -> wi 4   /\ wa 103

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107

This theorem depends on definitions:  df-bi 116

This theorem is referenced by:  th3q  6606  addnnnq0  7390  mulnnnq0  7391  addsrpr  7686  mulsrpr  7687  addccncf  13226