Theorem com15

Description: Commutation of antecedents. Swap 1st and 5th. (Contributed by Jeff Hankins, 28-Jun-2009) (Proof shortened by Wolf Lammen, 29-Jul-2012)

	Ref	Expression
Hypothesis	com5.1	⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → ( 𝜃 → ( 𝜏 → 𝜂 ) ) ) ) )
Assertion	com15	⊢ ( 𝜏 → ( 𝜓 → ( 𝜒 → ( 𝜃 → ( 𝜑 → 𝜂 ) ) ) ) )

Proof

Step	Hyp	Ref	Expression
1		com5.1	⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → ( 𝜃 → ( 𝜏 → 𝜂 ) ) ) ) )
2	1	com5l	⊢ ( 𝜓 → ( 𝜒 → ( 𝜃 → ( 𝜏 → ( 𝜑 → 𝜂 ) ) ) ) )
3	2	com4r	⊢ ( 𝜏 → ( 𝜓 → ( 𝜒 → ( 𝜃 → ( 𝜑 → 𝜂 ) ) ) ) )