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Mirrors > Home > MPE Home > Th. List > ustuqtop3 | Structured version Visualization version Unicode version |
Description: Lemma for ustuqtop 21316, similar to elnei 20182. (Contributed by Thierry Arnoux, 11-Jan-2018.) |
Ref | Expression |
---|---|
utopustuq.1 |
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Ref | Expression |
---|---|
ustuqtop3 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | fnresi 5719 |
. . . . . . 7
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
2 | fnsnfv 5953 |
. . . . . . 7
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3 | 1, 2 | mpan 681 |
. . . . . 6
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4 | 3 | ad4antlr 744 |
. . . . 5
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5 | simp-4l 781 |
. . . . . . 7
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6 | simplr 767 |
. . . . . . 7
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7 | ustdiag 21278 |
. . . . . . 7
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8 | 5, 6, 7 | syl2anc 671 |
. . . . . 6
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9 | imass1 5225 |
. . . . . 6
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10 | 8, 9 | syl 17 |
. . . . 5
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11 | 4, 10 | eqsstrd 3478 |
. . . 4
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12 | fvex 5902 |
. . . . 5
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13 | 12 | snss 4109 |
. . . 4
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14 | 11, 13 | sylibr 217 |
. . 3
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15 | fvresi 6119 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
16 | 15 | eqcomd 2468 |
. . . 4
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17 | 16 | ad4antlr 744 |
. . 3
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18 | simpr 467 |
. . 3
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19 | 14, 17, 18 | 3eltr4d 2555 |
. 2
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20 | vex 3060 |
. . . 4
![]() ![]() ![]() ![]() | |
21 | utopustuq.1 |
. . . . 5
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22 | 21 | ustuqtoplem 21309 |
. . . 4
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23 | 20, 22 | mpan2 682 |
. . 3
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24 | 23 | biimpa 491 |
. 2
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25 | 19, 24 | r19.29a 2944 |
1
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Colors of variables: wff setvar class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1680 ax-4 1693 ax-5 1769 ax-6 1816 ax-7 1862 ax-8 1900 ax-9 1907 ax-10 1926 ax-11 1931 ax-12 1944 ax-13 2102 ax-ext 2442 ax-rep 4531 ax-sep 4541 ax-nul 4550 ax-pow 4598 ax-pr 4656 ax-un 6615 |
This theorem depends on definitions: df-bi 190 df-or 376 df-an 377 df-3an 993 df-tru 1458 df-ex 1675 df-nf 1679 df-sb 1809 df-eu 2314 df-mo 2315 df-clab 2449 df-cleq 2455 df-clel 2458 df-nfc 2592 df-ne 2635 df-ral 2754 df-rex 2755 df-reu 2756 df-rab 2758 df-v 3059 df-sbc 3280 df-csb 3376 df-dif 3419 df-un 3421 df-in 3423 df-ss 3430 df-nul 3744 df-if 3894 df-pw 3965 df-sn 3981 df-pr 3983 df-op 3987 df-uni 4213 df-iun 4294 df-br 4419 df-opab 4478 df-mpt 4479 df-id 4771 df-xp 4862 df-rel 4863 df-cnv 4864 df-co 4865 df-dm 4866 df-rn 4867 df-res 4868 df-ima 4869 df-iota 5569 df-fun 5607 df-fn 5608 df-f 5609 df-f1 5610 df-fo 5611 df-f1o 5612 df-fv 5613 df-ust 21270 |
This theorem is referenced by: ustuqtop 21316 utopsnneiplem 21317 |
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