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  1889  ssel  3219  sscon  3339  uniss  3912  trel3  4193  copsexg  4334  ssopab2  4368  coss1  4883  fununi  5395  imadif  5407  fss  5491  ssimaex  5703  opabbrex  6060  ssoprab2  6072  poxp  6392  pmss12g  6839  ss2ixp  6875  xpdom2  7010  qbtwnxr  10507  ioc0  10512  climshftlemg  11853  bezoutlembz  12565  tgcl  14778  neipsm  14868  ssnei2  14871  tgcnp  14923  cnpnei  14933  cnptopco  14936  mopni3  15198  limcresi  15380  cnlimcim  15385