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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 1090 | . 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) ↔ (𝜓 ∧ 𝜑 ∧ 𝜒)) | |
2 | 3anrot 1092 | . 2 ⊢ ((𝜒 ∧ 𝜓 ∧ 𝜑) ↔ (𝜓 ∧ 𝜑 ∧ 𝜒)) | |
3 | 1, 2 | bitr4i 279 | 1 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) ↔ (𝜒 ∧ 𝜓 ∧ 𝜑)) |
Colors of variables: wff setvar class |
Syntax hints: ↔ wb 207 ∧ w3a 1079 |
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 208 df-an 397 df-3an 1081 |
This theorem is referenced by: an33rean 1474 nnmcan 8249 odupos 17733 wwlks2onsym 27664 frgr3v 27981 bnj345 31883 bnj1098 31954 pocnv 32896 btwnswapid2 33376 colinbtwnle 33476 uunT11p2 41009 uunT12p5 41015 uun2221p2 41026 |
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