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  4064  copsexg  4329  po3nr  4400  coss2  4877  fununi  5388  fiintim  7089  recexprlemlol  7809  recexprlemupu  7811  icoshft  10182  2ffzeq  10333  qbtwnxr  10472  ico0  10476  r19.2uz  11499  bezoutlemzz  12518  bezoutlemaz  12519  ptex  13292  rnglidlmmgm  14454  neiss  14818  uptx  14942  txcn  14943  bj-charfundcALT  16130