Theorem 3anrev 1099

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 1096	. 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) ↔ (𝜓 ∧ 𝜑 ∧ 𝜒))
2		3anrot 1098	. 2 ⊢ ((𝜒 ∧ 𝜓 ∧ 𝜑) ↔ (𝜓 ∧ 𝜑 ∧ 𝜒))
3	1, 2	bitr4i 277	1 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) ↔ (𝜒 ∧ 𝜓 ∧ 𝜑))

Syntax hints:   ↔ wb 205   ∧ w3a 1085

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  df-3an 1087

This theorem is referenced by:  an33rean  1481  an33reanOLD  1482  nnmcan  8427  odupos  17961  wwlks2onsym  28224  frgr3v  28540  bnj345  32593  bnj1098  32663  pocnv  33636  btwnswapid2  34247  colinbtwnle  34347  uunT11p2  42307  uunT12p5  42313  uun2221p2  42324