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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 5637. (Contributed by Scott Fenton, 11-Apr-2012.) |
Ref | Expression |
---|---|
brv | ⊢ 𝐴V𝐵 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | opex 5321 | . 2 ⊢ 〈𝐴, 𝐵〉 ∈ V | |
2 | df-br 5031 | . 2 ⊢ (𝐴V𝐵 ↔ 〈𝐴, 𝐵〉 ∈ V) | |
3 | 1, 2 | mpbir 234 | 1 ⊢ 𝐴V𝐵 |
Colors of variables: wff setvar class |
Syntax hints: ∈ wcel 2111 Vcvv 3441 〈cop 4531 class class class wbr 5030 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1797 ax-4 1811 ax-5 1911 ax-6 1970 ax-7 2015 ax-8 2113 ax-9 2121 ax-10 2142 ax-11 2158 ax-12 2175 ax-ext 2770 ax-sep 5167 ax-nul 5174 ax-pr 5295 |
This theorem depends on definitions: df-bi 210 df-an 400 df-or 845 df-3an 1086 df-tru 1541 df-ex 1782 df-nf 1786 df-sb 2070 df-clab 2777 df-cleq 2791 df-clel 2870 df-nfc 2938 df-v 3443 df-dif 3884 df-un 3886 df-in 3888 df-ss 3898 df-nul 4244 df-if 4426 df-sn 4526 df-pr 4528 df-op 4532 df-br 5031 |
This theorem is referenced by: brsset 33463 brtxpsd 33468 dffun10 33488 elfuns 33489 dfint3 33526 brub 33528 brvdif 35682 |
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