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  1865  ssel  3186  sscon  3306  uniss  3870  trel3  4149  copsexg  4287  ssopab2  4321  coss1  4832  fununi  5341  imadif  5353  fss  5436  ssimaex  5639  opabbrex  5988  ssoprab2  6000  poxp  6317  pmss12g  6761  ss2ixp  6797  xpdom2  6925  qbtwnxr  10398  ioc0  10403  climshftlemg  11584  bezoutlembz  12296  tgcl  14507  neipsm  14597  ssnei2  14600  tgcnp  14652  cnpnei  14662  cnptopco  14665  mopni3  14927  limcresi  15109  cnlimcim  15114