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  599  exdistrfor  1846  mopick2  2161  ssrexf  3286  ssrexv  3289  ssdif  3339  ssrin  3429  reupick  3488  disjss1  4065  copsexg  4330  po3nr  4401  coss2  4878  fununi  5389  fiintim  7104  recexprlemlol  7824  recexprlemupu  7826  icoshft  10198  2ffzeq  10349  qbtwnxr  10489  ico0  10493  r19.2uz  11519  bezoutlemzz  12538  bezoutlemaz  12539  ptex  13312  rnglidlmmgm  14475  neiss  14839  uptx  14963  txcn  14964  bj-charfundcALT  16227