Theorem an21 657

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 656	. 2 ⊢ ((𝜓 ∧ (𝜑 ∧ 𝜒)) ↔ ((𝜑 ∧ 𝜓) ∧ 𝜒))
3	2	bicomi 227	1 ⊢ (((𝜑 ∧ 𝜓) ∧ 𝜒) ↔ (𝜓 ∧ (𝜑 ∧ 𝜒)))

This proof depends on syntax axioms:   ↔ wb 209   ∧ wa 401

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 210  df-an 402

This theorem is used by:  an32  659  an13  660  indifdi  4242  fncnv  6643  mpocurryd  8324  rexuz2  13066  resmndismnd  19053  imasabl  20141  logfac2  27601  ltgov  29117  cgrabasimass  29435  brimg  36914  eldmqsres  39491  xrninxp2  39614