Theorem 3anrev 1047

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 1043	. 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) ↔ (𝜓 ∧ 𝜑 ∧ 𝜒))
2		3anrot 1041	. 2 ⊢ ((𝜒 ∧ 𝜓 ∧ 𝜑) ↔ (𝜓 ∧ 𝜑 ∧ 𝜒))
3	1, 2	bitr4i 267	1 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) ↔ (𝜒 ∧ 𝜓 ∧ 𝜑))

Syntax hints:   ↔ wb 196   ∧ w3a 1036

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 197  df-an 386  df-3an 1038

This theorem is referenced by:  3com13  1267  an33rean  1443  nnmcan  7659  odupos  17056  frgr3v  27003  bnj345  30484  bnj1098  30559  pocnv  31359  btwnswapid2  31764  colinbtwnle  31864  uunT11p2  38504  uunT12p5  38510  uun2221p2  38521