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Metamath Proof Explorer

Theorem 3com12

Description: Commutation in antecedent. Swap 1st and 2nd. (Contributed by NM, 28-Jan-1996) (Proof shortened by Andrew Salmon, 13-May-2011) (Proof shortened by Wolf Lammen, 22-Jun-2022)

		Ref	Expression
	Hypothesis	3exp.1	⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) → 𝜃 )
	Assertion	3com12	⊢ ( ( 𝜓 ∧ 𝜑 ∧ 𝜒 ) → 𝜃 )

Proof

Step	Hyp	Ref	Expression
1		3exp.1	⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) → 𝜃 )
2	1	3exp	⊢ ( 𝜑 → ( 𝜓 → ( 𝜒 → 𝜃 ) ) )
3	2	3imp21	⊢ ( ( 𝜓 ∧ 𝜑 ∧ 𝜒 ) → 𝜃 )