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  3217  ssrexv  3220  ssdif  3270  ssrin  3360  reupick  3419  disjss1  3986  copsexg  4244  po3nr  4310  coss2  4783  fununi  5284  fiintim  6927  recexprlemlol  7624  recexprlemupu  7626  icoshft  9988  2ffzeq  10138  qbtwnxr  10255  ico0  10259  r19.2uz  10997  bezoutlemzz  11997  bezoutlemaz  11998  neiss  13543  uptx  13667  txcn  13668  bj-charfundcALT  14443