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  597  exdistrfor  1822  mopick2  2136  ssrexf  3254  ssrexv  3257  ssdif  3307  ssrin  3397  reupick  3456  disjss1  4026  copsexg  4287  po3nr  4356  coss2  4833  fununi  5341  fiintim  7027  recexprlemlol  7738  recexprlemupu  7740  icoshft  10111  2ffzeq  10262  qbtwnxr  10398  ico0  10402  r19.2uz  11275  bezoutlemzz  12294  bezoutlemaz  12295  ptex  13067  rnglidlmmgm  14229  neiss  14593  uptx  14717  txcn  14718  bj-charfundcALT  15707