Theorem 3anim3i 1150

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 1147	1 ⊢ ((𝜒 ∧ 𝜃 ∧ 𝜑) → (𝜒 ∧ 𝜃 ∧ 𝜓))

Syntax hints:   → wi 4   ∧ w3a 1083

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 209  df-an 399  df-3an 1085

This theorem is referenced by:  syl3an3  1161  syl3anl3  1410  syl3anr3  1414  elioo4g  12800  ssnn0fi  13356  tmdcn2  22699  axcont  26764  numclwwlk3  28166  minvecolem3  28655  bnj556  32174  bnj557  32175  bnj1145  32267  btwnconn1lem4  33553  btwnconn1lem5  33554  btwnconn1lem6  33555  bj-ceqsalt  34204  bj-ceqsaltv  34205