Theorem 3anim1i 1138

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 1137	1 |- ((ph /\ ch /\ th) -> (ps /\ ch /\ th))

Syntax hints:   -> wi 4   /\ w3a 934

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  df-3an 936

This theorem is referenced by:  syl3an1  1215  syl3anl1  1230  syl3anr1  1234