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Mirrors > Home > MPE Home > Th. List > elwina | Structured version Visualization version Unicode version |
Description: Conditions of weak inaccessibility. (Contributed by Mario Carneiro, 22-Jun-2013.) |
Ref | Expression |
---|---|
elwina |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elex 3040 |
. 2
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2 | fvex 5889 |
. . . 4
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3 | eleq1 2537 |
. . . 4
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4 | 2, 3 | mpbii 216 |
. . 3
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5 | 4 | 3ad2ant2 1052 |
. 2
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6 | neeq1 2705 |
. . . 4
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7 | fveq2 5879 |
. . . . 5
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8 | eqeq12 2484 |
. . . . 5
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9 | 7, 8 | mpancom 682 |
. . . 4
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10 | rexeq 2974 |
. . . . 5
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11 | 10 | raleqbi1dv 2981 |
. . . 4
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12 | 6, 9, 11 | 3anbi123d 1365 |
. . 3
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13 | df-wina 9127 |
. . 3
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14 | 12, 13 | elab2g 3175 |
. 2
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15 | 1, 5, 14 | pm5.21nii 360 |
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 1677 ax-4 1690 ax-5 1766 ax-6 1813 ax-7 1859 ax-10 1932 ax-11 1937 ax-12 1950 ax-13 2104 ax-ext 2451 ax-nul 4527 |
This theorem depends on definitions: df-bi 190 df-or 377 df-an 378 df-3an 1009 df-tru 1455 df-ex 1672 df-nf 1676 df-sb 1806 df-eu 2323 df-clab 2458 df-cleq 2464 df-clel 2467 df-nfc 2601 df-ne 2643 df-ral 2761 df-rex 2762 df-rab 2765 df-v 3033 df-sbc 3256 df-dif 3393 df-un 3395 df-in 3397 df-ss 3404 df-nul 3723 df-if 3873 df-sn 3960 df-pr 3962 df-op 3966 df-uni 4191 df-br 4396 df-iota 5553 df-fv 5597 df-wina 9127 |
This theorem is referenced by: winaon 9131 inawina 9133 winacard 9135 winainf 9137 winalim2 9139 winafp 9140 gchina 9142 |
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