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Mirrors > Home > MPE Home > Th. List > Mathboxes > dfhe3 | Structured version Visualization version Unicode version |
Description: The property of relation
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Ref | Expression |
---|---|
dfhe3 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-he 36370 |
. 2
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2 | 19.21v 1790 |
. . . . . 6
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3 | 2 | bicomi 207 |
. . . . 5
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4 | 3 | albii 1695 |
. . . 4
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5 | alcom 1927 |
. . . 4
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6 | impexp 452 |
. . . . . . . 8
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7 | 6 | bicomi 207 |
. . . . . . 7
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8 | 7 | albii 1695 |
. . . . . 6
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9 | 19.23v 1822 |
. . . . . 6
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10 | 8, 9 | bitri 257 |
. . . . 5
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11 | 10 | albii 1695 |
. . . 4
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12 | 4, 5, 11 | 3bitri 279 |
. . 3
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13 | dfss2 3389 |
. . . . 5
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14 | vex 3016 |
. . . . . . . 8
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15 | opeq2 4137 |
. . . . . . . . . . . 12
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16 | 15 | eleq1d 2514 |
. . . . . . . . . . 11
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17 | df-br 4375 |
. . . . . . . . . . 11
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18 | 16, 17 | syl6bbr 271 |
. . . . . . . . . 10
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19 | 18 | anbi2d 715 |
. . . . . . . . 9
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20 | 19 | exbidv 1772 |
. . . . . . . 8
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21 | 14, 20 | elab 3153 |
. . . . . . 7
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22 | 21 | imbi1i 331 |
. . . . . 6
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23 | 22 | albii 1695 |
. . . . 5
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24 | 13, 23 | bitr2i 258 |
. . . 4
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25 | dfima3 5149 |
. . . . . 6
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26 | 25 | eqcomi 2461 |
. . . . 5
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27 | 26 | sseq1i 3424 |
. . . 4
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28 | 24, 27 | bitri 257 |
. . 3
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29 | 12, 28 | bitr2i 258 |
. 2
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30 | 1, 29 | bitri 257 |
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 1673 ax-4 1686 ax-5 1762 ax-6 1809 ax-7 1855 ax-9 1900 ax-10 1919 ax-11 1924 ax-12 1937 ax-13 2092 ax-ext 2432 ax-sep 4497 ax-nul 4506 ax-pr 4612 |
This theorem depends on definitions: df-bi 190 df-or 376 df-an 377 df-3an 988 df-tru 1451 df-ex 1668 df-nf 1672 df-sb 1802 df-eu 2304 df-mo 2305 df-clab 2439 df-cleq 2445 df-clel 2448 df-nfc 2582 df-ne 2624 df-ral 2742 df-rex 2743 df-rab 2746 df-v 3015 df-dif 3375 df-un 3377 df-in 3379 df-ss 3386 df-nul 3700 df-if 3850 df-sn 3937 df-pr 3939 df-op 3943 df-br 4375 df-opab 4434 df-xp 4818 df-cnv 4820 df-dm 4822 df-rn 4823 df-res 4824 df-ima 4825 df-he 36370 |
This theorem is referenced by: psshepw 36386 dffrege69 36530 |
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