Metamath Proof Explorer

Theorem syl5imp

Description: Closed form of syl5 . Derived automatically from syl5impVD . (Contributed by Alan Sare, 31-Dec-2011) (Proof modification is discouraged.) (New usage is discouraged.)

Ref Expression
Assertion syl5imp ⊢ φ → ψ → χ → θ → ψ → φ → θ → χ

Proof

Step Hyp Ref Expression
1 pm2.04 ⊢ φ → ψ → χ → ψ → φ → χ
2 1 imim2d ⊢ φ → ψ → χ → θ → ψ → θ → φ → χ
3 2 com34 ⊢ φ → ψ → χ → θ → ψ → φ → θ → χ