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Mirrors > Home > MPE Home > Th. List > elabrex | Structured version Visualization version Unicode version |
Description: Elementhood in an image set. (Contributed by Mario Carneiro, 14-Jan-2014.) |
Ref | Expression |
---|---|
elabrex.1 |
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Ref | Expression |
---|---|
elabrex |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | tru 1459 |
. . . 4
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2 | csbeq1a 3384 |
. . . . . . 7
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3 | 2 | equcoms 1875 |
. . . . . 6
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4 | a1tru 1471 |
. . . . . 6
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5 | 3, 4 | 2thd 248 |
. . . . 5
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6 | 5 | rspcev 3162 |
. . . 4
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7 | 1, 6 | mpan2 682 |
. . 3
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8 | elabrex.1 |
. . . 4
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9 | eqeq1 2466 |
. . . . 5
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10 | 9 | rexbidv 2913 |
. . . 4
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11 | 8, 10 | elab 3197 |
. . 3
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12 | 7, 11 | sylibr 217 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
13 | nfv 1772 |
. . . 4
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14 | nfcsb1v 3391 |
. . . . 5
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15 | 14 | nfeq2 2618 |
. . . 4
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16 | 2 | eqeq2d 2472 |
. . . 4
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17 | 13, 15, 16 | cbvrex 3028 |
. . 3
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18 | 17 | abbii 2578 |
. 2
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19 | 12, 18 | syl6eleqr 2551 |
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-10 1926 ax-11 1931 ax-12 1944 ax-13 2102 ax-ext 2442 |
This theorem depends on definitions: df-bi 190 df-or 376 df-an 377 df-tru 1458 df-ex 1675 df-nf 1679 df-sb 1809 df-clab 2449 df-cleq 2455 df-clel 2458 df-nfc 2592 df-ral 2754 df-rex 2755 df-v 3059 df-sbc 3280 df-csb 3376 |
This theorem is referenced by: eusvobj2 6308 lss1d 18235 prdsxmetlem 21432 prdsbl 21555 itg2monolem1 22757 heibor1 32187 dihglblem5 34911 |
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