Theorem anim1d 336

Description: Add a conjunct to right of antecedent and consequent in a deduction. (Contributed by NM, 3-Apr-1994.)

Hypothesis

Ref	Expression
anim1d.1	|- ( ph -> ( ps -> ch ) )

Assertion

Ref	Expression
anim1d	|- ( ph -> ( ( ps /\ th ) -> ( ch /\ th ) ) )

Proof of Theorem anim1d

Step	Hyp	Ref	Expression
1		anim1d.1	. 2 |- ( ph -> ( ps -> ch ) )
2		idd 21	. 2 |- ( ph -> ( th -> th ) )
3	1, 2	anim12d 335	1 |- ( ph -> ( ( ps /\ th ) -> ( ch /\ th ) ) )

Syntax hints:   -> wi 4   /\ wa 104

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

This theorem is referenced by:  pm3.45  601  exdistrfor  1849  mopick2  2164  ssrexf  3300  ssrexv  3303  ssdif  3354  ssrin  3446  reupick  3505  disjss1  4091  copsexg  4360  po3nr  4431  coss2  4911  fununi  5424  fiintim  7191  recexprlemlol  7941  recexprlemupu  7943  icoshft  10323  2ffzeq  10475  qbtwnxr  10617  ico0  10621  r19.2uz  11678  bezoutlemzz  12698  bezoutlemaz  12699  ptex  13477  rnglidlmmgm  14644  neiss  15015  uptx  15139  txcn  15140  bj-charfundcALT  16579