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Mathbox for Scott Fenton |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > brtxpsd | Structured version Visualization version Unicode version |
Description: Expansion of a common form used in quantifier-free definitions. (Contributed by Scott Fenton, 17-Apr-2014.) (Revised by Mario Carneiro, 19-Apr-2014.) |
Ref | Expression |
---|---|
brtxpsd.1 |
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brtxpsd.2 |
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Ref | Expression |
---|---|
brtxpsd |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-br 4402 |
. . 3
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2 | opex 4663 |
. . . . 5
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3 | 2 | elrn 5074 |
. . . 4
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4 | brsymdif 4458 |
. . . . . 6
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5 | brv 30637 |
. . . . . . . . 9
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6 | vex 3047 |
. . . . . . . . . 10
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7 | brtxpsd.1 |
. . . . . . . . . 10
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8 | brtxpsd.2 |
. . . . . . . . . 10
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9 | 6, 7, 8 | brtxp 30640 |
. . . . . . . . 9
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10 | 5, 9 | mpbiran 928 |
. . . . . . . 8
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11 | 8 | epelc 4746 |
. . . . . . . 8
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12 | 10, 11 | bitri 253 |
. . . . . . 7
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13 | brv 30637 |
. . . . . . . 8
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14 | 6, 7, 8 | brtxp 30640 |
. . . . . . . 8
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15 | 13, 14 | mpbiran2 929 |
. . . . . . 7
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16 | 12, 15 | bibi12i 317 |
. . . . . 6
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17 | 4, 16 | xchbinx 312 |
. . . . 5
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18 | 17 | exbii 1717 |
. . . 4
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19 | 3, 18 | bitri 253 |
. . 3
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20 | exnal 1698 |
. . 3
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21 | 1, 19, 20 | 3bitrri 276 |
. 2
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22 | 21 | con1bii 333 |
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 1668 ax-4 1681 ax-5 1757 ax-6 1804 ax-7 1850 ax-8 1888 ax-9 1895 ax-10 1914 ax-11 1919 ax-12 1932 ax-13 2090 ax-ext 2430 ax-sep 4524 ax-nul 4533 ax-pow 4580 ax-pr 4638 ax-un 6580 |
This theorem depends on definitions: df-bi 189 df-or 372 df-an 373 df-3an 986 df-tru 1446 df-ex 1663 df-nf 1667 df-sb 1797 df-eu 2302 df-mo 2303 df-clab 2437 df-cleq 2443 df-clel 2446 df-nfc 2580 df-ne 2623 df-ral 2741 df-rex 2742 df-rab 2745 df-v 3046 df-sbc 3267 df-dif 3406 df-un 3408 df-in 3410 df-ss 3417 df-symdif 3662 df-nul 3731 df-if 3881 df-sn 3968 df-pr 3970 df-op 3974 df-uni 4198 df-br 4402 df-opab 4461 df-mpt 4462 df-eprel 4744 df-id 4748 df-xp 4839 df-rel 4840 df-cnv 4841 df-co 4842 df-dm 4843 df-rn 4844 df-res 4845 df-iota 5545 df-fun 5583 df-fn 5584 df-f 5585 df-fo 5587 df-fv 5589 df-1st 6790 df-2nd 6791 df-txp 30613 |
This theorem is referenced by: brtxpsd2 30655 |
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