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Metamath Proof Explorer

Theorem 3comr

Description: Commutation in antecedent. Rotate right. (Contributed by NM, 28-Jan-1996) Theorems shortened and reordered. (Revised by Wolf Lammen, 9-Apr-2022)

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

Proof

Step	Hyp	Ref	Expression
1		3exp.1	⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) → 𝜃 )
2	1	3com12	⊢ ( ( 𝜓 ∧ 𝜑 ∧ 𝜒 ) → 𝜃 )
3	2	3com13	⊢ ( ( 𝜒 ∧ 𝜑 ∧ 𝜓 ) → 𝜃 )