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Metamath Proof Explorer

Theorem bnj170

Description: /\ -manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011) (Proof shortened by Andrew Salmon, 14-Jun-2011) (New usage is discouraged.)

		Ref	Expression
	Assertion	bnj170	⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) ↔ ( ( 𝜓 ∧ 𝜒 ) ∧ 𝜑 ) )

Proof

Step	Hyp	Ref	Expression
1		3anrot	⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) ↔ ( 𝜓 ∧ 𝜒 ∧ 𝜑 ) )
2		df-3an	⊢ ( ( 𝜓 ∧ 𝜒 ∧ 𝜑 ) ↔ ( ( 𝜓 ∧ 𝜒 ) ∧ 𝜑 ) )
3	1 2	bitri	⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) ↔ ( ( 𝜓 ∧ 𝜒 ) ∧ 𝜑 ) )