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Mirrors > Home > MPE Home > Th. List > brv | Structured version Visualization version GIF version |
Description: Two classes are always in relation by V. This is simply equivalent to 〈𝐴, 𝐵〉 ∈ V, and does not imply that V is a relation: see nrelv 5790. (Contributed by Scott Fenton, 11-Apr-2012.) |
Ref | Expression |
---|---|
brv | ⊢ 𝐴V𝐵 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | opex 5454 | . 2 ⊢ 〈𝐴, 𝐵〉 ∈ V | |
2 | df-br 5139 | . 2 ⊢ (𝐴V𝐵 ↔ 〈𝐴, 𝐵〉 ∈ V) | |
3 | 1, 2 | mpbir 230 | 1 ⊢ 𝐴V𝐵 |
Colors of variables: wff setvar class |
Syntax hints: ∈ wcel 2098 Vcvv 3466 〈cop 4626 class class class wbr 5138 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1789 ax-4 1803 ax-5 1905 ax-6 1963 ax-7 2003 ax-8 2100 ax-9 2108 ax-ext 2695 ax-sep 5289 ax-nul 5296 ax-pr 5417 |
This theorem depends on definitions: df-bi 206 df-an 396 df-or 845 df-3an 1086 df-tru 1536 df-fal 1546 df-ex 1774 df-sb 2060 df-clab 2702 df-cleq 2716 df-clel 2802 df-v 3468 df-dif 3943 df-un 3945 df-in 3947 df-ss 3957 df-nul 4315 df-if 4521 df-sn 4621 df-pr 4623 df-op 4627 df-br 5139 |
This theorem is referenced by: brsset 35356 brtxpsd 35361 dffun10 35381 elfuns 35382 dfint3 35419 brub 35421 brvdif 37619 |
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