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 → ( 𝜃 → 𝜏 ) ) ) )
Assertion	com14	⊢ ( 𝜃 → ( 𝜓 → ( 𝜒 → ( 𝜑 → 𝜏 ) ) ) )

Proof

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