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Mirrors > Home > MPE Home > Th. List > dfco2 | Structured version Visualization version Unicode version |
Description: Alternate definition of a class composition, using only one bound variable. (Contributed by NM, 19-Dec-2008.) |
Ref | Expression |
---|---|
dfco2 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | relco 5312 |
. 2
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2 | reliun 4932 |
. . 3
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3 | relxp 4920 |
. . . 4
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4 | 3 | a1i 11 |
. . 3
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5 | 2, 4 | mprgbir 2752 |
. 2
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6 | vex 3016 |
. . . 4
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7 | vex 3016 |
. . . 4
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8 | opelco2g 4980 |
. . . 4
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9 | 6, 7, 8 | mp2an 683 |
. . 3
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10 | eliun 4253 |
. . . 4
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11 | rexv 3030 |
. . . 4
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12 | opelxp 4842 |
. . . . . 6
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13 | vex 3016 |
. . . . . . . . 9
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14 | 13, 6 | elimasn 5171 |
. . . . . . . 8
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15 | 13, 6 | opelcnv 4994 |
. . . . . . . 8
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16 | 14, 15 | bitri 257 |
. . . . . . 7
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17 | 13, 7 | elimasn 5171 |
. . . . . . 7
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18 | 16, 17 | anbi12i 708 |
. . . . . 6
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19 | 12, 18 | bitri 257 |
. . . . 5
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20 | 19 | exbii 1722 |
. . . 4
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21 | 10, 11, 20 | 3bitrri 280 |
. . 3
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22 | 9, 21 | bitri 257 |
. 2
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23 | 1, 5, 22 | eqrelriiv 4907 |
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-sbc 3236 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-iun 4250 df-br 4375 df-opab 4434 df-xp 4818 df-rel 4819 df-cnv 4820 df-co 4821 df-dm 4822 df-rn 4823 df-res 4824 df-ima 4825 |
This theorem is referenced by: dfco2a 5314 |
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