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  1800  mopick2  2109  ssrexf  3218  ssrexv  3221  ssdif  3271  ssrin  3361  reupick  3420  disjss1  3987  copsexg  4245  po3nr  4311  coss2  4784  fununi  5285  fiintim  6928  recexprlemlol  7625  recexprlemupu  7627  icoshft  9990  2ffzeq  10141  qbtwnxr  10258  ico0  10262  r19.2uz  11002  bezoutlemzz  12003  bezoutlemaz  12004  ptex  12713  neiss  13653  uptx  13777  txcn  13778  bj-charfundcALT  14564