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  13324  ssnn0fi  13910  tmdcn2  24035  axcont  29030  numclwwlk3  30441  minvecolem3  30932  bnj556  35035  bnj557  35036  bnj1145  35128  btwnconn1lem4  36263  btwnconn1lem5  36264  btwnconn1lem6  36265  bj-ceqsalt  37060  bj-ceqsaltv  37061  uhgrimisgrgric  48214  clnbgr3stgrgrlim  48302