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 ) ) )

This proof depends on syntax axioms:   -> wi 4   /\ wa 104

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This proof depends on definitions:  df-bi 117

This theorem is used by:  pm3.45  605  exdistrfor  1853  mopick2  2170  ssrexf  3310  ssrexv  3313  ssdif  3364  ssrin  3456  reupick  3517  disjss1  4112  copsexg  4386  po3nr  4457  coss2  4938  fununi  5452  fiintim  7244  recexprlemlol  7999  recexprlemupu  8001  icoshft  10408  2ffzeq  10564  qbtwnxr  10708  ico0  10712  r19.2uz  11780  bezoutlemzz  12803  bezoutlemaz  12804  ptex  13676  rnglidlmmgm  14941  neiss  15393  uptx  15517  txcn  15518  bj-charfundcALT  17057