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Metamath Proof Explorer

Theorem an21

Description: Swap two conjuncts. (Contributed by Peter Mazsa, 18-Sep-2022)

Ref Expression
Assertion an21 ⊢ φ ∧ ψ ∧ χ ↔ ψ ∧ φ ∧ χ

Proof

Step Hyp Ref Expression
1 biid ⊢ φ ∧ χ ↔ φ ∧ χ
2 1 bianassc ⊢ ψ ∧ φ ∧ χ ↔ φ ∧ ψ ∧ χ
3 2 bicomi ⊢ φ ∧ ψ ∧ χ ↔ ψ ∧ φ ∧ χ