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Metamath Proof Explorer

Theorem 3anrev

Description: Reversal law for triple conjunction. (Contributed by NM, 21-Apr-1994)

Ref Expression
Assertion 3anrev ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) ↔ ( 𝜒 ∧ 𝜓 ∧ 𝜑 ) )

Proof

Step Hyp Ref Expression
1 3ancoma ⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) ↔ ( 𝜓 ∧ 𝜑 ∧ 𝜒 ) )
2 3anrot ⊢ ( ( 𝜒 ∧ 𝜓 ∧ 𝜑 ) ↔ ( 𝜓 ∧ 𝜑 ∧ 𝜒 ) )
3 1 2 bitr4i ⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) ↔ ( 𝜒 ∧ 𝜓 ∧ 𝜑 ) )