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  1848  mopick2  2163  ssrexf  3289  ssrexv  3292  ssdif  3342  ssrin  3432  reupick  3491  disjss1  4070  copsexg  4336  po3nr  4407  coss2  4886  fununi  5398  fiintim  7122  recexprlemlol  7845  recexprlemupu  7847  icoshft  10224  2ffzeq  10375  qbtwnxr  10516  ico0  10520  r19.2uz  11553  bezoutlemzz  12572  bezoutlemaz  12573  ptex  13346  rnglidlmmgm  14509  neiss  14873  uptx  14997  txcn  14998  bj-charfundcALT  16404