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Mirrors > Home > MPE Home > Th. List > elina | Structured version Visualization version Unicode version |
Description: Conditions of strong inaccessibility. (Contributed by Mario Carneiro, 22-Jun-2013.) |
Ref | Expression |
---|---|
elina |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elex 3054 |
. 2
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2 | fvex 5875 |
. . . 4
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3 | eleq1 2517 |
. . . 4
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4 | 2, 3 | mpbii 215 |
. . 3
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5 | 4 | 3ad2ant2 1030 |
. 2
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6 | neeq1 2686 |
. . . 4
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7 | fveq2 5865 |
. . . . 5
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8 | eqeq12 2464 |
. . . . 5
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9 | 7, 8 | mpancom 675 |
. . . 4
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10 | breq2 4406 |
. . . . 5
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11 | 10 | raleqbi1dv 2995 |
. . . 4
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12 | 6, 9, 11 | 3anbi123d 1339 |
. . 3
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13 | df-ina 9110 |
. . 3
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14 | 12, 13 | elab2g 3187 |
. 2
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15 | 1, 5, 14 | pm5.21nii 355 |
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 1669 ax-4 1682 ax-5 1758 ax-6 1805 ax-7 1851 ax-10 1915 ax-11 1920 ax-12 1933 ax-13 2091 ax-ext 2431 ax-nul 4534 |
This theorem depends on definitions: df-bi 189 df-or 372 df-an 373 df-3an 987 df-tru 1447 df-ex 1664 df-nf 1668 df-sb 1798 df-eu 2303 df-clab 2438 df-cleq 2444 df-clel 2447 df-nfc 2581 df-ne 2624 df-ral 2742 df-rex 2743 df-rab 2746 df-v 3047 df-sbc 3268 df-dif 3407 df-un 3409 df-in 3411 df-ss 3418 df-nul 3732 df-if 3882 df-sn 3969 df-pr 3971 df-op 3975 df-uni 4199 df-br 4403 df-iota 5546 df-fv 5590 df-ina 9110 |
This theorem is referenced by: inawina 9115 omina 9116 gchina 9124 inar1 9200 inatsk 9203 tskcard 9206 tskuni 9208 gruina 9243 grur1 9245 |
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