Theorem anim2d 337

Description: Add a conjunct to left of antecedent and consequent in a deduction. (Contributed by NM, 5-Aug-1993.)

Hypothesis

Ref	Expression
anim1d.1	|- ( ph -> ( ps -> ch ) )

Assertion

Ref	Expression
anim2d	|- ( ph -> ( ( th /\ ps ) -> ( th /\ ch ) ) )

Proof of Theorem anim2d

Step	Hyp	Ref	Expression
1		idd 21	. 2 |- ( ph -> ( th -> th ) )
2		anim1d.1	. 2 |- ( ph -> ( ps -> ch ) )
3	1, 2	anim12d 335	1 |- ( ph -> ( ( th /\ ps ) -> ( th /\ ch ) ) )

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:  spsbim  1896  ssel  3242  sscon  3363  ifeqeqxdc  3687  uniss  3956  trel3  4239  copsexg  4386  ssopab2  4420  coss1  4937  fununi  5452  imadif  5464  fss  5549  ssimaex  5767  opabbrex  6135  ssoprab2  6147  poxp  6472  pmss12g  6960  ss2ixp  6997  xpdom2  7133  qbtwnxr  10709  ioc0  10714  climshftlemg  12093  bezoutlembz  12806  tgcl  15290  neipsm  15380  ssnei2  15383  tgcnp  15435  cnpnei  15445  cnptopco  15448  mopni3  15710  limcresi  15892  cnlimcim  15897