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  3149  sscon  3269  uniss  3829  trel3  4107  copsexg  4242  ssopab2  4273  coss1  4779  fununi  5281  imadif  5293  fss  5374  ssimaex  5574  opabbrex  5914  ssoprab2  5926  poxp  6228  pmss12g  6670  ss2ixp  6706  xpdom2  6826  qbtwnxr  10251  ioc0  10256  climshftlemg  11301  bezoutlembz  11995  tgcl  13346  neipsm  13436  ssnei2  13439  tgcnp  13491  cnpnei  13501  cnptopco  13504  mopni3  13766  limcresi  13917  cnlimcim  13922