Theorem mp3an13 1364

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 1362	. 2 |- ( ( ph /\ ps ) -> th )
5	1, 4	mpan 424	1 |- ( ps -> th )

Syntax hints:   -> wi 4   /\ w3a 1004

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This theorem depends on definitions:  df-bi 117  df-3an 1006

This theorem is referenced by:  residfi  7139  pitonnlem1p1  8066  mulrid  8176  addltmul  9381  eluzaddi  9783  fz01en  10288  fznatpl1  10311  expubnd  10859  bernneq  10923  bernneq2  10924  efi4p  12280  efival  12295  cos2tsin  12314  cos01bnd  12321  cos01gt0  12326  dvds0  12369  odd2np1  12436  opoe  12458  gcdid  12559  pythagtriplem4  12843  fvpr0o  13426  fvpr1o  13427  blssioo  15280  tgioo  15281  rerestcntop  15285  rerest  15287  sinperlem  15535  sincosq1sgn  15553  sincosq2sgn  15554  sinq12gt0  15557  cosq14gt0  15559  1sgmprm  15721