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Metamath Proof Explorer

Theorem anim12dan

Description: Conjoin antecedents and consequents in a deduction. (Contributed by Jeff Madsen, 16-Jun-2011)

Ref Expression
Hypotheses anim12dan.1 ⊢ φ ∧ ψ → χ
anim12dan.2 ⊢ φ ∧ θ → τ
Assertion anim12dan ⊢ φ ∧ ψ ∧ θ → χ ∧ τ

Proof

Step Hyp Ref Expression
1 anim12dan.1 ⊢ φ ∧ ψ → χ
2 anim12dan.2 ⊢ φ ∧ θ → τ
3 1 ex ⊢ φ → ψ → χ
4 2 ex ⊢ φ → θ → τ
5 3 4 anim12d ⊢ φ → ψ ∧ θ → χ ∧ τ
6 5 imp ⊢ φ ∧ ψ ∧ θ → χ ∧ τ