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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 1482 nnmcan 8671 odupos 18386 wwlks2onsym 29988 frgr3v 30304 bnj345 34707 bnj1098 34776 pocnv 35743 btwnswapid2 36000 colinbtwnle 36100 uunT11p2 44796 uunT12p5 44802 uun2221p2 44813 grtriproplem 47844 grtrif1o 47847 |
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