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Metamath Proof Explorer

Theorem 3anim123i

Description: Join antecedents and consequents with conjunction. (Contributed by NM, 8-Apr-1994)

Ref Expression
Hypotheses 3anim123i.1 ⊢ φ → ψ
3anim123i.2 ⊢ χ → θ
3anim123i.3 ⊢ τ → η
Assertion 3anim123i ⊢ φ ∧ χ ∧ τ → ψ ∧ θ ∧ η

Proof

Step Hyp Ref Expression
1 3anim123i.1 ⊢ φ → ψ
2 3anim123i.2 ⊢ χ → θ
3 3anim123i.3 ⊢ τ → η
4 1 3ad2ant1 ⊢ φ ∧ χ ∧ τ → ψ
5 2 3ad2ant2 ⊢ φ ∧ χ ∧ τ → θ
6 3 3ad2ant3 ⊢ φ ∧ χ ∧ τ → η
7 4 5 6 3jca ⊢ φ ∧ χ ∧ τ → ψ ∧ θ ∧ η