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  1843  ssel  3150  sscon  3270  uniss  3831  trel3  4110  copsexg  4245  ssopab2  4276  coss1  4783  fununi  5285  imadif  5297  fss  5378  ssimaex  5578  opabbrex  5919  ssoprab2  5931  poxp  6233  pmss12g  6675  ss2ixp  6711  xpdom2  6831  qbtwnxr  10258  ioc0  10263  climshftlemg  11310  bezoutlembz  12005  tgcl  13567  neipsm  13657  ssnei2  13660  tgcnp  13712  cnpnei  13722  cnptopco  13725  mopni3  13987  limcresi  14138  cnlimcim  14143