Theorem 3anim2i 1151

Description: Add two conjuncts to antecedent and consequent. (Contributed by AV, 21-Nov-2019.)

Hypothesis

Ref	Expression
3animi.1	⊢ (𝜑 → 𝜓)

Assertion

Ref	Expression
3anim2i	⊢ ((𝜒 ∧ 𝜑 ∧ 𝜃) → (𝜒 ∧ 𝜓 ∧ 𝜃))

Proof of Theorem 3anim2i

Step	Hyp	Ref	Expression
1		id 22	. 2 ⊢ (𝜒 → 𝜒)
2		3animi.1	. 2 ⊢ (𝜑 → 𝜓)
3		id 22	. 2 ⊢ (𝜃 → 𝜃)
4	1, 2, 3	3anim123i 1149	1 ⊢ ((𝜒 ∧ 𝜑 ∧ 𝜃) → (𝜒 ∧ 𝜓 ∧ 𝜃))

Syntax hints:   → wi 4   ∧ w3a 1085

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 206  df-an 396  df-3an 1087

This theorem is referenced by:  syl3an2  1162  syl3anl2  1411  syl3anr2  1415  elfzo0z  13357  swrdfv0  14290  mdetunilem9  21677  chpdmat  21898  subgrprop2  27544  welb  35821  lincreslvec3  45711