Metamath Proof Explorer


Theorem 3anim2i

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

Ref Expression
Hypothesis 3animi.1 ⊢ ( 𝜑 → 𝜓 )
Assertion 3anim2i ( ( 𝜒 ∧ 𝜑 ∧ 𝜃 ) → ( 𝜒 ∧ 𝜓 ∧ 𝜃 ) )

Proof

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