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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 1038 | . 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) ↔ (𝜓 ∧ 𝜑 ∧ 𝜒)) | |
2 | 3anrot 1036 | . 2 ⊢ ((𝜒 ∧ 𝜓 ∧ 𝜑) ↔ (𝜓 ∧ 𝜑 ∧ 𝜒)) | |
3 | 1, 2 | bitr4i 266 | 1 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) ↔ (𝜒 ∧ 𝜓 ∧ 𝜑)) |
Colors of variables: wff setvar class |
Syntax hints: ↔ wb 195 ∧ w3a 1031 |
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 196 df-an 385 df-3an 1033 |
This theorem is referenced by: 3com13 1262 an33rean 1438 nnmcan 7601 odupos 16958 frgra3v 26529 bnj345 30033 bnj1098 30108 pocnv 30907 btwnswapid2 31295 colinbtwnle 31395 uunT11p2 38046 uunT12p5 38052 uun2221p2 38063 frgr3v 41445 |
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