Theorem com25

Description: Commutation of antecedents. Swap 2nd and 5th. Deduction associated with com14 . (Contributed by Jeff Hankins, 28-Jun-2009)

	Ref	Expression
Hypothesis	com5.1	⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → ( 𝜃 → ( 𝜏 → 𝜂 ) ) ) ) )
Assertion	com25	⊢ ( 𝜑 → ( 𝜏 → ( 𝜒 → ( 𝜃 → ( 𝜓 → 𝜂 ) ) ) ) )

Proof

Step	Hyp	Ref	Expression
1		com5.1	⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → ( 𝜃 → ( 𝜏 → 𝜂 ) ) ) ) )
2	1	com24	⊢ ( 𝜑 → ( 𝜃 → ( 𝜒 → ( 𝜓 → ( 𝜏 → 𝜂 ) ) ) ) )
3	2	com45	⊢ ( 𝜑 → ( 𝜃 → ( 𝜒 → ( 𝜏 → ( 𝜓 → 𝜂 ) ) ) ) )
4	3	com24	⊢ ( 𝜑 → ( 𝜏 → ( 𝜒 → ( 𝜃 → ( 𝜓 → 𝜂 ) ) ) ) )