Metamath Proof Explorer


Theorem com14

Description: Commutation of antecedents. Swap 1st and 4th. (Contributed by NM, 25-Apr-1994) (Proof shortened by Wolf Lammen, 28-Jul-2012)

Ref Expression
Hypothesis com4.1 ( 𝜑 → ( 𝜓 → ( 𝜒 → ( 𝜃𝜏 ) ) ) )
Assertion com14 ( 𝜃 → ( 𝜓 → ( 𝜒 → ( 𝜑𝜏 ) ) ) )

Proof

Step Hyp Ref Expression
1 com4.1 ( 𝜑 → ( 𝜓 → ( 𝜒 → ( 𝜃𝜏 ) ) ) )
2 1 com4l ( 𝜓 → ( 𝜒 → ( 𝜃 → ( 𝜑𝜏 ) ) ) )
3 2 com3r ( 𝜃 → ( 𝜓 → ( 𝜒 → ( 𝜑𝜏 ) ) ) )