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Mirrors > Home > ILE Home > Th. List > 2basgeng | Unicode version |
Description: Conditions that determine the equality of two generated topologies. (Contributed by NM, 8-May-2007.) (Revised by Jim Kingdon, 5-Mar-2023.) |
Ref | Expression |
---|---|
2basgeng |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | tgvalex 12734 |
. . . . 5
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2 | 1 | 3ad2ant1 1020 |
. . . 4
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3 | simp3 1001 |
. . . 4
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4 | 2, 3 | ssexd 4158 |
. . 3
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5 | simp2 1000 |
. . 3
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6 | tgss 13960 |
. . 3
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7 | 4, 5, 6 | syl2anc 411 |
. 2
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8 | simp1 999 |
. . . 4
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9 | tgss3 13975 |
. . . 4
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10 | 4, 8, 9 | syl2anc 411 |
. . 3
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11 | 3, 10 | mpbird 167 |
. 2
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12 | 7, 11 | eqssd 3187 |
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 710 ax-5 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-10 1516 ax-11 1517 ax-i12 1518 ax-bndl 1520 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 ax-13 2162 ax-14 2163 ax-ext 2171 ax-sep 4136 ax-pow 4189 ax-pr 4224 ax-un 4448 |
This theorem depends on definitions: df-bi 117 df-3an 982 df-tru 1367 df-nf 1472 df-sb 1774 df-eu 2041 df-mo 2042 df-clab 2176 df-cleq 2182 df-clel 2185 df-nfc 2321 df-ral 2473 df-rex 2474 df-v 2754 df-sbc 2978 df-un 3148 df-in 3150 df-ss 3157 df-pw 3592 df-sn 3613 df-pr 3614 df-op 3616 df-uni 3825 df-iun 3903 df-br 4019 df-opab 4080 df-mpt 4081 df-id 4308 df-xp 4647 df-rel 4648 df-cnv 4649 df-co 4650 df-dm 4651 df-iota 5193 df-fun 5233 df-fv 5239 df-topgen 12731 |
This theorem is referenced by: txbasval 14164 tgioo 14443 tgqioo 14444 |
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