Theorem 3anim1i 1216

Description: Add two conjuncts to antecedent and consequent. (Contributed by Jeff Hankins, 16-Aug-2009.)

Hypothesis

Ref	Expression
3animi.1	|- ( ph -> ps )

Assertion

Ref	Expression
3anim1i	|- ( ( ph /\ ch /\ th ) -> ( ps /\ ch /\ th ) )

Proof of Theorem 3anim1i

Step	Hyp	Ref	Expression
1		3animi.1	. 2 |- ( ph -> ps )
2		id 19	. 2 |- ( ch -> ch )
3		id 19	. 2 |- ( th -> th )
4	1, 2, 3	3anim123i 1215	1 |- ( ( ph /\ ch /\ th ) -> ( ps /\ ch /\ th ) )

This proof depends on syntax axioms:   -> wi 4   /\ w3a 1009

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This proof depends on definitions:  df-bi 117  df-3an 1011

This theorem is used by:  syl3an1  1311  syl3anl1  1326  syl3anr1  1330  elioc2  10338  elico2  10339  elicc2  10340  dvdsleabs2  12613  subrngringnsg  14513