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Mirrors > Home > MPE Home > Th. List > Mathboxes > gneispace2 | Structured version Visualization version Unicode version |
Description: The predicate that is a (generic) Seifert And Threlfall neighborhood space. (Contributed by RP, 15-Apr-2021.) |
Ref | Expression |
---|---|
gneispace.a |
Ref | Expression |
---|---|
gneispace2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | id 22 | . . . 4 | |
2 | dmeq 5324 | . . . 4 | |
3 | 2 | pweqd 4163 | . . . . . . 7 |
4 | 3 | difeq1d 3727 | . . . . . 6 |
5 | 4 | pweqd 4163 | . . . . 5 |
6 | 5 | difeq1d 3727 | . . . 4 |
7 | 1, 2, 6 | feq123d 6034 | . . 3 |
8 | fveq1 6190 | . . . . 5 | |
9 | 8 | eleq2d 2687 | . . . . . . . 8 |
10 | 9 | imbi2d 330 | . . . . . . 7 |
11 | 3, 10 | raleqbidv 3152 | . . . . . 6 |
12 | 11 | anbi2d 740 | . . . . 5 |
13 | 8, 12 | raleqbidv 3152 | . . . 4 |
14 | 2, 13 | raleqbidv 3152 | . . 3 |
15 | 7, 14 | anbi12d 747 | . 2 |
16 | gneispace.a | . 2 | |
17 | 15, 16 | elab2g 3353 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 196 wa 384 wceq 1483 wcel 1990 cab 2608 wral 2912 cdif 3571 wss 3574 c0 3915 cpw 4158 csn 4177 cdm 5114 wf 5884 cfv 5888 |
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-pw 4160 df-sn 4178 df-pr 4180 df-op 4184 df-uni 4437 df-br 4654 df-opab 4713 df-rel 5121 df-cnv 5122 df-co 5123 df-dm 5124 df-rn 5125 df-iota 5851 df-fun 5890 df-fn 5891 df-f 5892 df-fv 5896 |
This theorem is referenced by: gneispace3 38431 gneispacef 38433 gneispaceel 38441 gneispacess 38443 |
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