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Mirrors > Home > NFE Home > Th. List > iinab | Unicode version |
Description: Indexed intersection of a class builder. (Contributed by NM, 6-Dec-2011.) |
Ref | Expression |
---|---|
iinab |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfcv 2490 |
. . . 4
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2 | nfab1 2492 |
. . . 4
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3 | 1, 2 | nfiin 3997 |
. . 3
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4 | nfab1 2492 |
. . 3
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5 | 3, 4 | cleqf 2514 |
. 2
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6 | abid 2341 |
. . . 4
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7 | 6 | ralbii 2639 |
. . 3
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8 | vex 2863 |
. . . 4
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9 | eliin 3975 |
. . . 4
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10 | 8, 9 | ax-mp 5 |
. . 3
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11 | abid 2341 |
. . 3
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12 | 7, 10, 11 | 3bitr4i 268 |
. 2
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13 | 5, 12 | mpgbir 1550 |
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 1546 ax-5 1557 ax-17 1616 ax-9 1654 ax-8 1675 ax-6 1729 ax-7 1734 ax-11 1746 ax-12 1925 ax-ext 2334 |
This theorem depends on definitions: df-bi 177 df-or 359 df-an 360 df-tru 1319 df-ex 1542 df-nf 1545 df-sb 1649 df-clab 2340 df-cleq 2346 df-clel 2349 df-nfc 2479 df-ral 2620 df-v 2862 df-iin 3973 |
This theorem is referenced by: iinrab 4029 |
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