Theorem mp3anl3 1228

Description: An inference based on modus ponens. (Contributed by NM, 24-Feb-2005.)

Hypotheses

Ref	Expression
mp3anl3.1	|- ch
mp3anl3.2	|- ( ( ( ph /\ ps /\ ch ) /\ th ) -> ta )

Assertion

Ref	Expression
mp3anl3	|- ( ( ( ph /\ ps ) /\ th ) -> ta )

Proof of Theorem mp3anl3

Step	Hyp	Ref	Expression
1		mp3anl3.1	. . 3 |- ch
2		mp3anl3.2	. . . 4 |- ( ( ( ph /\ ps /\ ch ) /\ th ) -> ta )
3	2	ex 108	. . 3 |- ( ( ph /\ ps /\ ch ) -> ( th -> ta ) )
4	1, 3	mp3an3 1221	. 2 |- ( ( ph /\ ps ) -> ( th -> ta ) )
5	4	imp 115	1 |- ( ( ( ph /\ ps ) /\ th ) -> ta )

Syntax hints:   -> wi 4   /\ wa 97   /\ w3a 885

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101

This theorem depends on definitions:  df-bi 110  df-3an 887

This theorem is referenced by:  mp3anr3  1231