Theorem anim2d 330

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 328	1 |- ( ph -> ( ( th /\ ps ) -> ( th /\ ch ) ) )

Syntax hints:   -> wi 4   /\ wa 102

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106

This theorem depends on definitions:  df-bi 115

This theorem is referenced by:  spsbim  1764  ssel  2993  sscon  3106  uniss  3622  trel3  3883  copsexg  3999  ssopab2  4030  coss1  4509  fununi  4987  imadif  4999  fss  5074  ssimaex  5255  opabbrex  5569  ssoprab2  5581  poxp  5873  xpdom2  6328  qbtwnxr  9266  ioc0  9271  climshftlemg  10141  bezoutlembz  10393