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Mirrors > Home > MPE Home > Th. List > isnrm | Structured version Visualization version Unicode version |
Description: The predicate "is a normal space." Much like the case for regular spaces, normal does not imply Hausdorff or even regular. (Contributed by Jeff Hankins, 1-Feb-2010.) (Revised by Mario Carneiro, 24-Aug-2015.) |
Ref | Expression |
---|---|
isnrm |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | fveq2 6191 | . . . . 5 | |
2 | 1 | ineq1d 3813 | . . . 4 |
3 | fveq2 6191 | . . . . . . . 8 | |
4 | 3 | fveq1d 6193 | . . . . . . 7 |
5 | 4 | sseq1d 3632 | . . . . . 6 |
6 | 5 | anbi2d 740 | . . . . 5 |
7 | 6 | rexeqbi1dv 3147 | . . . 4 |
8 | 2, 7 | raleqbidv 3152 | . . 3 |
9 | 8 | raleqbi1dv 3146 | . 2 |
10 | df-nrm 21121 | . 2 | |
11 | 9, 10 | elrab2 3366 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wb 196 wa 384 wceq 1483 wcel 1990 wral 2912 wrex 2913 cin 3573 wss 3574 cpw 4158 cfv 5888 ctop 20698 ccld 20820 ccl 20822 cnrm 21114 |
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 |
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-uni 4437 df-br 4654 df-iota 5851 df-fv 5896 df-nrm 21121 |
This theorem is referenced by: nrmtop 21140 nrmsep3 21159 isnrm2 21162 kqnrmlem1 21546 kqnrmlem2 21547 nrmhmph 21597 |
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