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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 5843 | . 2 ⊢ (𝑅 ↾ 𝐶) ⊆ 𝑅 | |
2 | 1 | ssbri 5075 | 1 ⊢ (𝐴(𝑅 ↾ 𝐶)𝐵 → 𝐴𝑅𝐵) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∈ wcel 2111 Vcvv 3441 class class class wbr 5030 ↾ cres 5521 |
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-ext 2770 |
This theorem depends on definitions: df-bi 210 df-an 400 df-ex 1782 df-sb 2070 df-clab 2777 df-cleq 2791 df-clel 2870 df-v 3443 df-in 3888 df-ss 3898 df-br 5031 df-res 5531 |
This theorem is referenced by: (None) |
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