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Mirrors > Home > ILE Home > Th. List > istopg | Unicode version |
Description: Express the predicate
"![]()
Note: In the literature, a topology is often represented by a
calligraphic letter T, which resembles the letter J. This confusion may
have led to J being used by some authors (e.g., K. D. Joshi,
Introduction to General Topology (1983), p. 114) and it is
convenient
for us since we later use |
Ref | Expression |
---|---|
istopg |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pweq 3579 |
. . . . 5
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2 | eleq2 2241 |
. . . . 5
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3 | 1, 2 | raleqbidv 2685 |
. . . 4
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4 | eleq2 2241 |
. . . . . 6
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5 | 4 | raleqbi1dv 2681 |
. . . . 5
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6 | 5 | raleqbi1dv 2681 |
. . . 4
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7 | 3, 6 | anbi12d 473 |
. . 3
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8 | df-top 13501 |
. . 3
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9 | 7, 8 | elab2g 2885 |
. 2
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10 | df-ral 2460 |
. . . 4
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11 | elpw2g 4157 |
. . . . . 6
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12 | 11 | imbi1d 231 |
. . . . 5
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13 | 12 | albidv 1824 |
. . . 4
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14 | 10, 13 | bitrid 192 |
. . 3
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15 | 14 | anbi1d 465 |
. 2
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16 | 9, 15 | bitrd 188 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-io 709 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-ext 2159 ax-sep 4122 |
This theorem depends on definitions: df-bi 117 df-tru 1356 df-nf 1461 df-sb 1763 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-ral 2460 df-v 2740 df-in 3136 df-ss 3143 df-pw 3578 df-top 13501 |
This theorem is referenced by: istopfin 13503 uniopn 13504 inopn 13506 tgcl 13567 distop 13588 epttop 13593 |
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