Theorem an21 656

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 264	. . 3 ⊢ ((𝜑 ∧ 𝜒) ↔ (𝜑 ∧ 𝜒))
2	1	bianassc 655	. 2 ⊢ ((𝜓 ∧ (𝜑 ∧ 𝜒)) ↔ ((𝜑 ∧ 𝜓) ∧ 𝜒))
3	2	bicomi 227	1 ⊢ (((𝜑 ∧ 𝜓) ∧ 𝜒) ↔ (𝜓 ∧ (𝜑 ∧ 𝜒)))

Syntax hints:   ↔ wb 209   ∧ wa 400

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 210  df-an 401

This theorem is referenced by:  an32  658  an13  659  indifdi  4255  fncnv  6610  mpocurryd  8264  rexuz2  12922  resmndismnd  18865  imasabl  19945  logfac2  27346  ltgov  28831  brimg  36325  eldmqsres  38831  xrninxp2  38954