Theorem 3anim2i 1091

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 19	. 2 ⊢ (𝜒 → 𝜒)
2		3animi.1	. 2 ⊢ (𝜑 → 𝜓)
3		id 19	. 2 ⊢ (𝜃 → 𝜃)
4	1, 2, 3	3anim123i 1089	1 ⊢ ((𝜒 ∧ 𝜑 ∧ 𝜃) → (𝜒 ∧ 𝜓 ∧ 𝜃))

Syntax hints:   → wi 4   ∧ w3a 885

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101

This theorem depends on definitions:  df-bi 110  df-3an 887

This theorem is referenced by:  elfzo0z  9040