Theorem an21 468

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

Assertion

Ref	Expression
an21	⊢ (((𝜑 ∧ 𝜓) ∧ 𝜒) ↔ (𝜓 ∧ (𝜑 ∧ 𝜒)))

Proof of Theorem an21

Step	Hyp	Ref	Expression
1		biid 170	. . 3 ⊢ ((𝜑 ∧ 𝜒) ↔ (𝜑 ∧ 𝜒))
2	1	bianassc 467	. 2 ⊢ ((𝜓 ∧ (𝜑 ∧ 𝜒)) ↔ ((𝜑 ∧ 𝜓) ∧ 𝜒))
3	2	bicomi 131	1 ⊢ (((𝜑 ∧ 𝜓) ∧ 𝜒) ↔ (𝜓 ∧ (𝜑 ∧ 𝜒)))

Syntax hints:   ∧ wa 103   ↔ wb 104

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107

This theorem depends on definitions:  df-bi 116

This theorem is referenced by: (None)