Metamath Proof Explorer


Theorem com35

Description: Commutation of antecedents. Swap 3rd and 5th. Deduction associated with com24 . Double deduction associated with com13 . (Contributed by Jeff Hankins, 28-Jun-2009)

Ref Expression
Hypothesis com5.1 ⊢ φ → ψ → χ → θ → τ → η
Assertion com35 ⊢ φ → ψ → τ → θ → χ → η

Proof

Step Hyp Ref Expression
1 com5.1 ⊢ φ → ψ → χ → θ → τ → η
2 1 com34 ⊢ φ → ψ → θ → χ → τ → η
3 2 com45 ⊢ φ → ψ → θ → τ → χ → η
4 3 com34 ⊢ φ → ψ → τ → θ → χ → η