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 ) ) )

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:  spsbim  1896  ssel  3242  sscon  3363  ifeqeqxdc  3684  uniss  3951  trel3  4232  copsexg  4379  ssopab2  4413  coss1  4930  fununi  5444  imadif  5456  fss  5541  ssimaex  5758  opabbrex  6122  ssoprab2  6134  poxp  6458  pmss12g  6946  ss2ixp  6983  xpdom2  7119  qbtwnxr  10670  ioc0  10675  climshftlemg  12046  bezoutlembz  12759  tgcl  15088  neipsm  15178  ssnei2  15181  tgcnp  15233  cnpnei  15243  cnptopco  15246  mopni3  15508  limcresi  15690  cnlimcim  15695