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| Mirrors > Home > MPE Home > Th. List > 3anrev | Structured version Visualization version GIF version | ||
| Description: Reversal law for triple conjunction. (Contributed by NM, 21-Apr-1994.) | 
| Ref | Expression | 
|---|---|
| 3anrev | ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) ↔ (𝜒 ∧ 𝜓 ∧ 𝜑)) | 
| 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 278 | 1 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) ↔ (𝜒 ∧ 𝜓 ∧ 𝜑)) | 
| Colors of variables: wff setvar class | 
| Syntax hints: ↔ wb 206 ∧ 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 207 df-an 396 df-3an 1088 | 
| This theorem is referenced by: an33rean 1484 nnmcan 8673 odupos 18374 wwlks2onsym 29979 frgr3v 30295 bnj345 34729 bnj1098 34798 pocnv 35764 btwnswapid2 36020 colinbtwnle 36120 uunT11p2 44823 uunT12p5 44829 uun2221p2 44840 grtriproplem 47911 grtrif1o 47914 | 
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