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Mathbox for Scott Fenton |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > distel | Structured version Visualization version Unicode version |
Description: Distinctors in terms of membership. (NOTE: this only works with relations where we can prove el 4602 and elirrv 8143.) (Contributed by Scott Fenton, 15-Dec-2010.) |
Ref | Expression |
---|---|
distel |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | el 4602 |
. . 3
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2 | df-ex 1675 |
. . . 4
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3 | nfnae 2163 |
. . . . . 6
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4 | dveel1 2210 |
. . . . . . . 8
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5 | 3, 4 | nfd 1967 |
. . . . . . 7
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6 | 5 | nfnd 1995 |
. . . . . 6
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7 | elequ2 1912 |
. . . . . . . 8
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8 | 7 | notbid 300 |
. . . . . . 7
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9 | 8 | a1i 11 |
. . . . . 6
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10 | 3, 6, 9 | cbvald 2129 |
. . . . 5
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11 | 10 | notbid 300 |
. . . 4
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12 | 2, 11 | syl5bb 265 |
. . 3
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13 | 1, 12 | mpbii 216 |
. 2
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14 | elirrv 8143 |
. . . . 5
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15 | elequ1 1905 |
. . . . 5
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16 | 14, 15 | mtbii 308 |
. . . 4
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17 | 16 | alimi 1695 |
. . 3
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18 | 17 | con3i 142 |
. 2
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19 | 13, 18 | impbii 192 |
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-sep 4541 ax-nul 4550 ax-pow 4598 ax-pr 4656 ax-reg 8138 |
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-ne 2635 df-ral 2754 df-rex 2755 df-v 3059 df-dif 3419 df-un 3421 df-nul 3744 df-sn 3981 df-pr 3983 |
This theorem is referenced by: (None) |
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