![]() |
Mathbox for Jeff Madsen |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > MPE Home > Th. List > Mathboxes > brresi2 | Structured version Visualization version GIF version |
Description: Restriction of a binary relation. (Contributed by Jeff Madsen, 2-Sep-2009.) |
Ref | Expression |
---|---|
brresi2.1 | ⊢ 𝐵 ∈ V |
Ref | Expression |
---|---|
brresi2 | ⊢ (𝐴(𝑅 ↾ 𝐶)𝐵 → 𝐴𝑅𝐵) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | resss 6021 | . 2 ⊢ (𝑅 ↾ 𝐶) ⊆ 𝑅 | |
2 | 1 | ssbri 5192 | 1 ⊢ (𝐴(𝑅 ↾ 𝐶)𝐵 → 𝐴𝑅𝐵) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∈ wcel 2105 Vcvv 3477 class class class wbr 5147 ↾ cres 5690 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1791 ax-4 1805 ax-5 1907 ax-6 1964 ax-7 2004 ax-8 2107 ax-9 2115 ax-ext 2705 |
This theorem depends on definitions: df-bi 207 df-an 396 df-tru 1539 df-ex 1776 df-sb 2062 df-clab 2712 df-cleq 2726 df-clel 2813 df-v 3479 df-in 3969 df-ss 3979 df-br 5148 df-res 5700 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |