Theorem 3anim2i 1169

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 23	. 2 ⊢ (𝜒 → 𝜒)
2		3animi.1	. 2 ⊢ (𝜑 → 𝜓)
3		id 23	. 2 ⊢ (𝜃 → 𝜃)
4	1, 2, 3	3anim123i 1167	1 ⊢ ((𝜒 ∧ 𝜑 ∧ 𝜃) → (𝜒 ∧ 𝜓 ∧ 𝜃))

Syntax hints:   → wi 4   ∧ w3a 1101

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 210  df-an 401  df-3an 1103

This theorem is referenced by:  syl3an2  1180  syl3anl2  1438  syl3anr2  1442  elfzo0z  13730  swrdfv0  14687  mdetunilem9  22746  chpdmat  22967  subgrprop2  29565  welb  38275  lincreslvec3  49147