Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
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 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | tgvalex 12591 | . . . . 5 | |
2 | 1 | 3ad2ant1 1007 | . . . 4 |
3 | simp3 988 | . . . 4 | |
4 | 2, 3 | ssexd 4116 | . . 3 |
5 | simp2 987 | . . 3 | |
6 | tgss 12604 | . . 3 | |
7 | 4, 5, 6 | syl2anc 409 | . 2 |
8 | simp1 986 | . . . 4 | |
9 | tgss3 12619 | . . . 4 | |
10 | 4, 8, 9 | syl2anc 409 | . . 3 |
11 | 3, 10 | mpbird 166 | . 2 |
12 | 7, 11 | eqssd 3154 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 104 w3a 967 wceq 1342 wcel 2135 cvv 2721 wss 3111 cfv 5182 ctg 12507 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 699 ax-5 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-10 1492 ax-11 1493 ax-i12 1494 ax-bndl 1496 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 ax-13 2137 ax-14 2138 ax-ext 2146 ax-sep 4094 ax-pow 4147 ax-pr 4181 ax-un 4405 |
This theorem depends on definitions: df-bi 116 df-3an 969 df-tru 1345 df-nf 1448 df-sb 1750 df-eu 2016 df-mo 2017 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-ral 2447 df-rex 2448 df-v 2723 df-sbc 2947 df-un 3115 df-in 3117 df-ss 3124 df-pw 3555 df-sn 3576 df-pr 3577 df-op 3579 df-uni 3784 df-iun 3862 df-br 3977 df-opab 4038 df-mpt 4039 df-id 4265 df-xp 4604 df-rel 4605 df-cnv 4606 df-co 4607 df-dm 4608 df-iota 5147 df-fun 5184 df-fv 5190 df-topgen 12513 |
This theorem is referenced by: txbasval 12808 tgioo 13087 tgqioo 13088 |
Copyright terms: Public domain | W3C validator |