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Metamath Proof Explorer

Theorem syl6c

Description: Inference combining syl6 with contraction. (Contributed by Alan Sare, 2-May-2011)

Ref Expression
Hypotheses syl6c.1 ⊢ φ → ψ → χ
syl6c.2 ⊢ φ → ψ → θ
syl6c.3 ⊢ χ → θ → τ
Assertion syl6c ⊢ φ → ψ → τ

Proof

Step Hyp Ref Expression
1 syl6c.1 ⊢ φ → ψ → χ
2 syl6c.2 ⊢ φ → ψ → θ
3 syl6c.3 ⊢ χ → θ → τ
4 1 3 syl6 ⊢ φ → ψ → θ → τ
5 2 4 mpdd ⊢ φ → ψ → τ