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Metamath Proof Explorer

Theorem com24

Description: Commutation of antecedents. Swap 2nd and 4th. Deduction associated with com13 . (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	com24	⊢ ( 𝜑 → ( 𝜃 → ( 𝜒 → ( 𝜓 → 𝜏 ) ) ) )

Proof

Step	Hyp	Ref	Expression
1		com4.1	⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → ( 𝜃 → 𝜏 ) ) ) )
2	1	com4t	⊢ ( 𝜒 → ( 𝜃 → ( 𝜑 → ( 𝜓 → 𝜏 ) ) ) )
3	2	com13	⊢ ( 𝜑 → ( 𝜃 → ( 𝜒 → ( 𝜓 → 𝜏 ) ) ) )