Theorem anim1i 551

Description: Introduce conjunct to both sides of an implication. (Contributed by NM, 5-Aug-1993.)

Hypothesis

Ref	Expression
anim1i.1	|- (ph -> ps)

Assertion

Ref	Expression
anim1i	|- ((ph /\ ch) -> (ps /\ ch))

Proof of Theorem anim1i

Step	Hyp	Ref	Expression
1		anim1i.1	. 2 |- (ph -> ps)
2		id 19	. 2 |- (ch -> ch)
3	1, 2	anim12i 549	1 |- ((ph /\ ch) -> (ps /\ ch))

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:  sylanl1  631  sylanr1  633  disamis  2314  sucevenodd  4511  sucoddeven  4512  fun11uni  5163  fores  5279  isomin  5497  ndmovass  5619