Theorem 3com13

Description: Commutation in antecedent. Swap 1st and 3rd. (Contributed by NM, 28-Jan-1996) (Proof shortened by Wolf Lammen, 22-Jun-2022)

	Ref	Expression
Hypothesis	3exp.1	⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) → 𝜃 )
Assertion	3com13	⊢ ( ( 𝜒 ∧ 𝜓 ∧ 𝜑 ) → 𝜃 )

Proof

Step	Hyp	Ref	Expression
1		3exp.1	⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) → 𝜃 )
2	1	3exp	⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → 𝜃 ) ) )
3	2	3imp31	⊢ ( ( 𝜒 ∧ 𝜓 ∧ 𝜑 ) → 𝜃 )