Theorem 3anrev 1100

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 1097	. 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) ↔ (𝜓 ∧ 𝜑 ∧ 𝜒))
2		3anrot 1099	. 2 ⊢ ((𝜒 ∧ 𝜓 ∧ 𝜑) ↔ (𝜓 ∧ 𝜑 ∧ 𝜒))
3	1, 2	bitr4i 277	1 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) ↔ (𝜒 ∧ 𝜓 ∧ 𝜑))

Syntax hints:   ↔ wb 205   ∧ w3a 1086

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 397  df-3an 1088

This theorem is referenced by:  an33rean  1482  an33reanOLD  1483  nnmcan  8465  odupos  18046  wwlks2onsym  28323  frgr3v  28639  bnj345  32693  bnj1098  32763  pocnv  33730  btwnswapid2  34320  colinbtwnle  34420  uunT11p2  42418  uunT12p5  42424  uun2221p2  42435