Metamath Proof Explorer


Theorem 3anim3i

Description: Add two conjuncts to antecedent and consequent. (Contributed by Jeff Hankins, 19-Aug-2009)

Ref Expression
Hypothesis 3animi.1 ⊢ φ → ψ
Assertion 3anim3i ⊢ χ ∧ θ ∧ φ → χ ∧ θ ∧ ψ

Proof

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