Theorem 3anim1i 1187

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 1186	1 |- ( ( ph /\ ch /\ th ) -> ( ps /\ ch /\ th ) )

Syntax hints:   -> wi 4   /\ w3a 980

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  df-3an 982

This theorem is referenced by:  syl3an1  1282  syl3anl1  1297  syl3anr1  1301  elioc2  10028  elico2  10029  elicc2  10030  dvdsleabs2  12028  subrngringnsg  13837