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Mirrors > Home > NFE Home > Th. List > iinxprg | Unicode version |
Description: Indexed intersection with an unordered pair index. (Contributed by NM, 25-Jan-2012.) |
Ref | Expression |
---|---|
iinxprg.1 |
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iinxprg.2 |
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Ref | Expression |
---|---|
iinxprg |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | iinxprg.1 |
. . . . 5
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2 | 1 | eleq2d 2420 |
. . . 4
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3 | iinxprg.2 |
. . . . 5
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4 | 3 | eleq2d 2420 |
. . . 4
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5 | 2, 4 | ralprg 3775 |
. . 3
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6 | vex 2862 |
. . . 4
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7 | eliin 3974 |
. . . 4
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8 | 6, 7 | ax-mp 8 |
. . 3
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9 | elin 3219 |
. . 3
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10 | 5, 8, 9 | 3bitr4g 279 |
. 2
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11 | 10 | eqrdv 2351 |
1
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Colors of variables: wff setvar class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-3 7 ax-mp 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-3an 936 df-nan 1288 df-tru 1319 df-ex 1542 df-nf 1545 df-sb 1649 df-clab 2340 df-cleq 2346 df-clel 2349 df-nfc 2478 df-ral 2619 df-v 2861 df-sbc 3047 df-nin 3211 df-compl 3212 df-in 3213 df-un 3214 df-sn 3741 df-pr 3742 df-iin 3972 |
This theorem is referenced by: (None) |
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