Theorem mp3an13 1259

Description: An inference based on modus ponens. (Contributed by NM, 14-Jul-2005.)

Hypotheses

Ref	Expression
mp3an13.1	|- ph
mp3an13.2	|- ch
mp3an13.3	|- ( ( ph /\ ps /\ ch ) -> th )

Assertion

Ref	Expression
mp3an13	|- ( ps -> th )

Proof of Theorem mp3an13

Step	Hyp	Ref	Expression
1		mp3an13.1	. 2 |- ph
2		mp3an13.2	. . 3 |- ch
3		mp3an13.3	. . 3 |- ( ( ph /\ ps /\ ch ) -> th )
4	2, 3	mp3an3 1257	. 2 |- ( ( ph /\ ps ) -> th )
5	1, 4	mpan 414	1 |- ( ps -> th )

Syntax hints:   -> wi 4   /\ w3a 919

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106

This theorem depends on definitions:  df-bi 115  df-3an 921

This theorem is referenced by:  pitonnlem1p1  7014  mulid1  7116  addltmul  8267  eluzaddi  8645  fz01en  9072  fznatpl1  9093  expubnd  9533  bernneq  9593  bernneq2  9594  dvds0  10210  odd2np1  10272  opoe  10295  gcdid  10377