Theorem 3anim3i 1155

Description: Add two conjuncts to antecedent and consequent. (Contributed by Jeff Hankins, 19-Aug-2009.)

Hypothesis

Ref	Expression
3animi.1	⊢ (𝜑 → 𝜓)

Assertion

Ref	Expression
3anim3i	⊢ ((𝜒 ∧ 𝜃 ∧ 𝜑) → (𝜒 ∧ 𝜃 ∧ 𝜓))

Proof of Theorem 3anim3i

Step	Hyp	Ref	Expression
1		id 22	. 2 ⊢ (𝜒 → 𝜒)
2		id 22	. 2 ⊢ (𝜃 → 𝜃)
3		3animi.1	. 2 ⊢ (𝜑 → 𝜓)
4	1, 2, 3	3anim123i 1152	1 ⊢ ((𝜒 ∧ 𝜃 ∧ 𝜑) → (𝜒 ∧ 𝜃 ∧ 𝜓))

Syntax hints:   → wi 4   ∧ w3a 1087

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 207  df-an 396  df-3an 1089

This theorem is referenced by:  syl3an3  1166  syl3anl3  1417  syl3anr3  1421  elioo4g  13336  ssnn0fi  13922  tmdcn2  24050  axcont  29067  numclwwlk3  30478  minvecolem3  30970  bnj556  35082  bnj557  35083  bnj1145  35175  btwnconn1lem4  36312  btwnconn1lem5  36313  btwnconn1lem6  36314  bj-ceqsalt  37161  bj-ceqsaltv  37162  uhgrimisgrgric  48320  clnbgr3stgrgrlim  48408