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  1891  ssel  3221  sscon  3341  uniss  3914  trel3  4195  copsexg  4336  ssopab2  4370  coss1  4885  fununi  5398  imadif  5410  fss  5494  ssimaex  5707  opabbrex  6064  ssoprab2  6076  poxp  6396  pmss12g  6843  ss2ixp  6879  xpdom2  7014  qbtwnxr  10516  ioc0  10521  climshftlemg  11862  bezoutlembz  12574  tgcl  14787  neipsm  14877  ssnei2  14880  tgcnp  14932  cnpnei  14942  cnptopco  14945  mopni3  15207  limcresi  15389  cnlimcim  15394