Theorem mp3anl3 1273

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 423	. . 3 |- ((ph /\ ps /\ ch) -> (th -> ta))
4	1, 3	mp3an3 1266	. 2 |- ((ph /\ ps) -> (th -> ta))
5	4	imp 418	1 |- (((ph /\ ps) /\ th) -> ta)

Syntax hints:   -> wi 4   /\ wa 358   /\ w3a 934

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 177  df-an 360  df-3an 936

This theorem is referenced by:  mp3anr3  1276