Theorem com4l

Description: Commutation of antecedents. Rotate left. (Contributed by NM, 25-Apr-1994) (Proof shortened by Mel L. O'Cat, 15-Aug-2004)

	Ref	Expression
Hypothesis	com4.1	⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → ( 𝜃 → 𝜏 ) ) ) )
Assertion	com4l	⊢ ( 𝜓 → ( 𝜒 → ( 𝜃 → ( 𝜑 → 𝜏 ) ) ) )

Proof

Step	Hyp	Ref	Expression
1		com4.1	⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → ( 𝜃 → 𝜏 ) ) ) )
2	1	com3l	⊢ ( 𝜓 → ( 𝜒 → ( 𝜑 → ( 𝜃 → 𝜏 ) ) ) )
3	2	com34	⊢ ( 𝜓 → ( 𝜒 → ( 𝜃 → ( 𝜑 → 𝜏 ) ) ) )