Theorem com34

Description: Commutation of antecedents. Swap 3rd and 4th. Deduction associated with com23 . Double deduction associated with com12 . (Contributed by NM, 25-Apr-1994)

	Ref	Expression
Hypothesis	com4.1	⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → ( 𝜃 → 𝜏 ) ) ) )
Assertion	com34	⊢ ( 𝜑 → ( 𝜓 → ( 𝜃 → ( 𝜒 → 𝜏 ) ) ) )

Proof

Step	Hyp	Ref	Expression
1		com4.1	⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → ( 𝜃 → 𝜏 ) ) ) )
2		pm2.04	⊢ ( ( 𝜒 → ( 𝜃 → 𝜏 ) ) → ( 𝜃 → ( 𝜒 → 𝜏 ) ) )
3	1 2	syl6	⊢ ( 𝜑 → ( 𝜓 → ( 𝜃 → ( 𝜒 → 𝜏 ) ) ) )