Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > MPE Home > Th. List > eldmressnsn | Structured version Visualization version Unicode version |
Description: The element of the domain of a restriction to a singleton is the element of the singleton. (Contributed by Alexander van der Vekens, 2-Jul-2017.) |
Ref | Expression |
---|---|
eldmressnsn |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | snidg 4206 | . 2 | |
2 | dmressnsn 5438 | . 2 | |
3 | 1, 2 | eleqtrrd 2704 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wcel 1990 csn 4177 cdm 5114 cres 5116 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 ax-sep 4781 ax-nul 4789 ax-pr 4906 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-3an 1039 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-ral 2917 df-rex 2918 df-rab 2921 df-v 3202 df-dif 3577 df-un 3579 df-in 3581 df-ss 3588 df-nul 3916 df-if 4087 df-sn 4178 df-pr 4180 df-op 4184 df-br 4654 df-opab 4713 df-xp 5120 df-dm 5124 df-res 5126 |
This theorem is referenced by: eldmeldmressn 5440 fvn0fvelrn 6430 dfdfat2 41211 |
Copyright terms: Public domain | W3C validator |