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Mathbox for Alexander van der Vekens |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > dmressnsn | Structured version Unicode version |
Description: The domain of a restriction to a singleton is a singleton. (Contributed by Alexander van der Vekens, 2-Jul-2017.) |
Ref | Expression |
---|---|
dmressnsn |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dmres 5229 |
. 2
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2 | snssi 4115 |
. . 3
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3 | df-ss 3440 |
. . 3
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4 | 2, 3 | sylib 196 |
. 2
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5 | 1, 4 | syl5eq 2504 |
1
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Colors of variables: wff setvar class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1592 ax-4 1603 ax-5 1671 ax-6 1710 ax-7 1730 ax-9 1762 ax-10 1777 ax-11 1782 ax-12 1794 ax-13 1952 ax-ext 2430 ax-sep 4511 ax-nul 4519 ax-pr 4629 |
This theorem depends on definitions: df-bi 185 df-or 370 df-an 371 df-3an 967 df-tru 1373 df-ex 1588 df-nf 1591 df-sb 1703 df-clab 2437 df-cleq 2443 df-clel 2446 df-nfc 2601 df-ne 2646 df-ral 2800 df-rex 2801 df-rab 2804 df-v 3070 df-dif 3429 df-un 3431 df-in 3433 df-ss 3440 df-nul 3736 df-if 3890 df-sn 3976 df-pr 3978 df-op 3982 df-br 4391 df-opab 4449 df-xp 4944 df-dm 4948 df-res 4950 |
This theorem is referenced by: eldmressnsn 30167 funcoressn 30171 funressnfv 30172 |
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