Theorem 3anrev 1101

Description: Reversal law for triple conjunction. (Contributed by NM, 21-Apr-1994.)

Assertion

Ref	Expression
3anrev	⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) ↔ (𝜒 ∧ 𝜓 ∧ 𝜑))

Proof of Theorem 3anrev

Step	Hyp	Ref	Expression
1		3ancoma 1098	. 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) ↔ (𝜓 ∧ 𝜑 ∧ 𝜒))
2		3anrot 1100	. 2 ⊢ ((𝜒 ∧ 𝜓 ∧ 𝜑) ↔ (𝜓 ∧ 𝜑 ∧ 𝜒))
3	1, 2	bitr4i 278	1 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) ↔ (𝜒 ∧ 𝜓 ∧ 𝜑))

Syntax hints:   ↔ wb 206   ∧ w3a 1087

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 207  df-an 396  df-3an 1089

This theorem is referenced by:  an33rean  1486  nnmcan  8572  odupos  18261  wwlks2onsym  30045  frgr3v  30362  bnj345  34891  bnj1098  34960  pocnv  35979  btwnswapid2  36234  colinbtwnle  36334  uunT11p2  45153  uunT12p5  45159  uun2221p2  45170  grtriproplem  48299  grtrif1o  48302