Theorem anim1d 547

Description: Add a conjunct to right of antecedent and consequent in a deduction. (Contributed by NM, 3-Apr-1994.)

Hypothesis

Ref	Expression
anim1d.1	|- (ph -> (ps -> ch))

Assertion

Ref	Expression
anim1d	|- (ph -> ((ps /\ th) -> (ch /\ th)))

Proof of Theorem anim1d

Step	Hyp	Ref	Expression
1		anim1d.1	. 2 |- (ph -> (ps -> ch))
2		idd 21	. 2 |- (ph -> (th -> th))
3	1, 2	anim12d 546	1 |- (ph -> ((ps /\ th) -> (ch /\ th)))

Syntax hints:   -> wi 4   /\ wa 358

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 177  df-an 360

This theorem is referenced by:  pm3.45  807  ax12olem2  1928  exdistrf  1971  mopick2  2271  ssrexv  3332  ssdif  3402  ssrin  3481  reupick  3540  copsexg  4608  coss2  4874  fununi  5161  fnfreclem3  6320