Theorem 3anim3i 1154

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 1151	1 ⊢ ((𝜒 ∧ 𝜃 ∧ 𝜑) → (𝜒 ∧ 𝜃 ∧ 𝜓))

Syntax hints:   → wi 4   ∧ w3a 1086

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 1088

This theorem is referenced by:  syl3an3  1165  syl3anl3  1416  syl3anr3  1420  elioo4g  13345  ssnn0fi  13928  tmdcn2  24010  axcont  28957  numclwwlk3  30365  minvecolem3  30856  bnj556  34884  bnj557  34885  bnj1145  34977  btwnconn1lem4  36072  btwnconn1lem5  36073  btwnconn1lem6  36074  bj-ceqsalt  36868  bj-ceqsaltv  36869  uhgrimisgrgric  47925