Metamath Proof Explorer


Theorem com13

Description: Commutation of antecedents. Swap 1st and 3rd. (Contributed by NM, 25-Apr-1994) (Proof shortened by Wolf Lammen, 28-Jul-2012)

Ref Expression
Hypothesis com3.1 ( 𝜑 → ( 𝜓 → ( 𝜒𝜃 ) ) )
Assertion com13 ( 𝜒 → ( 𝜓 → ( 𝜑𝜃 ) ) )

Proof

Step Hyp Ref Expression
1 com3.1 ( 𝜑 → ( 𝜓 → ( 𝜒𝜃 ) ) )
2 1 com3r ( 𝜒 → ( 𝜑 → ( 𝜓𝜃 ) ) )
3 2 com23 ( 𝜒 → ( 𝜓 → ( 𝜑𝜃 ) ) )