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Mirrors > Home > ILE Home > Th. List > toptopon | Unicode version |
Description: Alternative definition of in terms of TopOn. (Contributed by Mario Carneiro, 13-Aug-2015.) |
Ref | Expression |
---|---|
toptopon.1 |
Ref | Expression |
---|---|
toptopon | TopOn |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | toptopon.1 | . . 3 | |
2 | istopon 12558 | . . 3 TopOn | |
3 | 1, 2 | mpbiran2 930 | . 2 TopOn |
4 | 3 | bicomi 131 | 1 TopOn |
Colors of variables: wff set class |
Syntax hints: wb 104 wceq 1342 wcel 2135 cuni 3783 cfv 5182 ctop 12542 TopOnctopon 12555 |
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-rab 2451 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-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-topon 12556 |
This theorem is referenced by: toptopon2 12564 eltpsi 12586 restuni 12719 stoig 12720 iscn2 12747 lmcvg 12764 cnpnei 12766 cnss1 12773 cnss2 12774 cncnpi 12775 cncnp2m 12778 cnnei 12779 cnrest 12782 cnrest2 12783 cnrest2r 12784 cnptoprest 12786 cnptoprest2 12787 lmss 12793 txuni 12810 txcnmpt 12820 txcn 12822 cnmpt11 12830 cnmpt11f 12831 imasnopn 12846 hmeof1o 12856 hmeores 12862 txhmeo 12866 retopon 13073 |
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