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  3218  sscon  3338  uniss  3908  trel3  4189  copsexg  4329  ssopab2  4363  coss1  4876  fununi  5388  imadif  5400  fss  5484  ssimaex  5694  opabbrex  6047  ssoprab2  6059  poxp  6376  pmss12g  6820  ss2ixp  6856  xpdom2  6986  qbtwnxr  10472  ioc0  10477  climshftlemg  11808  bezoutlembz  12520  tgcl  14732  neipsm  14822  ssnei2  14825  tgcnp  14877  cnpnei  14887  cnptopco  14890  mopni3  15152  limcresi  15334  cnlimcim  15339