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Metamath Proof Explorer

Theorem anim12d

Description: Conjoin antecedents and consequents in a deduction. (Contributed by NM, 3-Apr-1994) (Proof shortened by Wolf Lammen, 18-Dec-2013)

Ref Expression
Hypotheses anim12d.1 ⊢ φ → ψ → χ
anim12d.2 ⊢ φ → θ → τ
Assertion anim12d ⊢ φ → ψ ∧ θ → χ ∧ τ

Proof

Step Hyp Ref Expression
1 anim12d.1 ⊢ φ → ψ → χ
2 anim12d.2 ⊢ φ → θ → τ
3 idd ⊢ φ → χ ∧ τ → χ ∧ τ
4 1 2 3 syl2and ⊢ φ → ψ ∧ θ → χ ∧ τ