Theorem an21 643

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 261	. . 3 ⊢ ((𝜑 ∧ 𝜒) ↔ (𝜑 ∧ 𝜒))
2	1	bianassc 642	. 2 ⊢ ((𝜓 ∧ (𝜑 ∧ 𝜒)) ↔ ((𝜑 ∧ 𝜓) ∧ 𝜒))
3	2	bicomi 223	1 ⊢ (((𝜑 ∧ 𝜓) ∧ 𝜒) ↔ (𝜓 ∧ (𝜑 ∧ 𝜒)))

Syntax hints:   ↔ wb 205   ∧ wa 395

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 206  df-an 396

This theorem is referenced by:  an32  645  an13  646  indifdi  4279  fncnv  6620  mpocurryd  8268  rexuz2  12907  resmndismnd  18753  imasabl  19824  logfac2  27143  ltgov  28394  brimg  35527  eldmqsres  37753  xrninxp2  37859