Theorem com13

Description: Commutation of antecedents. Swap 1st and 3rd. (Contributed by NM, 25-Apr-1994) (Proof shortened by Wolf Lammen, 28-Jul-2012)

	Ref	Expression
Hypothesis	com3.1	⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → 𝜃 ) ) )
Assertion	com13	⊢ ( 𝜒 → ( 𝜓 → ( 𝜑 → 𝜃 ) ) )

Proof

Step	Hyp	Ref	Expression
1		com3.1	⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → 𝜃 ) ) )
2	1	com3r	⊢ ( 𝜒 → ( 𝜑 → ( 𝜓 → 𝜃 ) ) )
3	2	com23	⊢ ( 𝜒 → ( 𝜓 → ( 𝜑 → 𝜃 ) ) )