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Metamath Proof Explorer

Theorem anim12d1

Description: Variant of anim12d where the second implication does not depend on the antecedent. (Contributed by Rodolfo Medina, 12-Oct-2010)

Ref Expression
Hypotheses anim12d1.1 ⊢ φ → ψ → χ
anim12d1.2 ⊢ θ → τ
Assertion anim12d1 ⊢ φ → ψ ∧ θ → χ ∧ τ

Proof

Step Hyp Ref Expression
1 anim12d1.1 ⊢ φ → ψ → χ
2 anim12d1.2 ⊢ θ → τ
3 2 a1i ⊢ φ → θ → τ
4 1 3 anim12d ⊢ φ → ψ ∧ θ → χ ∧ τ