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Mirrors > Home > MPE Home > Th. List > ustbas | Structured version Visualization version Unicode version |
Description: Recover the base of an uniform structure . UnifOn is to UnifOn what is to TopOn. (Contributed by Thierry Arnoux, 16-Nov-2017.) |
Ref | Expression |
---|---|
ustbas.1 |
Ref | Expression |
---|---|
ustbas | UnifOn UnifOn |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ustfn 22005 | . . . 4 UnifOn | |
2 | fnfun 5988 | . . . 4 UnifOn UnifOn | |
3 | elunirn 6509 | . . . 4 UnifOn UnifOn UnifOn UnifOn | |
4 | 1, 2, 3 | mp2b 10 | . . 3 UnifOn UnifOn UnifOn |
5 | ustbas2 22029 | . . . . . . . 8 UnifOn | |
6 | ustbas.1 | . . . . . . . 8 | |
7 | 5, 6 | syl6eqr 2674 | . . . . . . 7 UnifOn |
8 | 7 | fveq2d 6195 | . . . . . 6 UnifOn UnifOn UnifOn |
9 | 8 | eleq2d 2687 | . . . . 5 UnifOn UnifOn UnifOn |
10 | 9 | ibi 256 | . . . 4 UnifOn UnifOn |
11 | 10 | rexlimivw 3029 | . . 3 UnifOn UnifOn UnifOn |
12 | 4, 11 | sylbi 207 | . 2 UnifOn UnifOn |
13 | elrnust 22028 | . 2 UnifOn UnifOn | |
14 | 12, 13 | impbii 199 | 1 UnifOn UnifOn |
Colors of variables: wff setvar class |
Syntax hints: wb 196 wceq 1483 wcel 1990 wrex 2913 cvv 3200 cuni 4436 cdm 5114 crn 5115 wfun 5882 wfn 5883 cfv 5888 UnifOncust 22003 |
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-8 1992 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 ax-sep 4781 ax-nul 4789 ax-pow 4843 ax-pr 4906 ax-un 6949 |
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-eu 2474 df-mo 2475 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-ne 2795 df-ral 2917 df-rex 2918 df-rab 2921 df-v 3202 df-sbc 3436 df-csb 3534 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-mpt 4730 df-id 5024 df-xp 5120 df-rel 5121 df-cnv 5122 df-co 5123 df-dm 5124 df-rn 5125 df-res 5126 df-iota 5851 df-fun 5890 df-fn 5891 df-fv 5896 df-ust 22004 |
This theorem is referenced by: (None) |
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