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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 5736. (Contributed by Scott Fenton, 11-Apr-2012.) |
Ref | Expression |
---|---|
brv | ⊢ 𝐴V𝐵 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | opex 5403 | . 2 ⊢ ⟨𝐴, 𝐵⟩ ∈ V | |
2 | df-br 5090 | . 2 ⊢ (𝐴V𝐵 ↔ ⟨𝐴, 𝐵⟩ ∈ V) | |
3 | 1, 2 | mpbir 230 | 1 ⊢ 𝐴V𝐵 |
Colors of variables: wff setvar class |
Syntax hints: ∈ wcel 2105 Vcvv 3441 ⟨cop 4578 class class class wbr 5089 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1796 ax-4 1810 ax-5 1912 ax-6 1970 ax-7 2010 ax-8 2107 ax-9 2115 ax-ext 2707 ax-sep 5240 ax-nul 5247 ax-pr 5369 |
This theorem depends on definitions: df-bi 206 df-an 397 df-or 845 df-3an 1088 df-tru 1543 df-fal 1553 df-ex 1781 df-sb 2067 df-clab 2714 df-cleq 2728 df-clel 2814 df-v 3443 df-dif 3900 df-un 3902 df-in 3904 df-ss 3914 df-nul 4269 df-if 4473 df-sn 4573 df-pr 4575 df-op 4579 df-br 5090 |
This theorem is referenced by: brsset 34282 brtxpsd 34287 dffun10 34307 elfuns 34308 dfint3 34345 brub 34347 brvdif 36519 |
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