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Metamath Proof Explorer

Theorem anim12ii

Description: Conjoin antecedents and consequents in a deduction. (Contributed by NM, 11-Nov-2007) (Proof shortened by Wolf Lammen, 19-Jul-2013)

Ref Expression
Hypotheses anim12ii.1 ⊢ φ → ψ → χ
anim12ii.2 ⊢ θ → ψ → τ
Assertion anim12ii ⊢ φ ∧ θ → ψ → χ ∧ τ

Proof

Step Hyp Ref Expression
1 anim12ii.1 ⊢ φ → ψ → χ
2 anim12ii.2 ⊢ θ → ψ → τ
3 pm3.43 ⊢ ψ → χ ∧ ψ → τ → ψ → χ ∧ τ
4 1 2 3 syl2an ⊢ φ ∧ θ → ψ → χ ∧ τ