Theorem com23

Description: Commutation of antecedents. Swap 2nd and 3rd. Deduction associated with com12 . (Contributed by NM, 27-Dec-1992) (Proof shortened by Wolf Lammen, 4-Aug-2012)

	Ref	Expression
Hypothesis	com3.1	⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → 𝜃 ) ) )
Assertion	com23	⊢ ( 𝜑 → ( 𝜒 → ( 𝜓 → 𝜃 ) ) )

Proof

Step	Hyp	Ref	Expression
1		com3.1	⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → 𝜃 ) ) )
2		pm2.27	⊢ ( 𝜒 → ( ( 𝜒 → 𝜃 ) → 𝜃 ) )
3	1 2	syl9	⊢ ( 𝜑 → ( 𝜒 → ( 𝜓 → 𝜃 ) ) )