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Mirrors > Home > NFE Home > Th. List > sfineq2 | Unicode version |
Description: Equality theorem for the finite S relationship. (Contributed by SF, 27-Jan-2015.) |
Ref | Expression |
---|---|
sfineq2 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eleq1 2413 |
. . 3
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2 | eleq2 2414 |
. . . . 5
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3 | 2 | anbi2d 684 |
. . . 4
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4 | 3 | exbidv 1626 |
. . 3
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5 | 1, 4 | 3anbi23d 1255 |
. 2
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6 | df-sfin 4447 |
. 2
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7 | df-sfin 4447 |
. 2
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8 | 5, 6, 7 | 3bitr4g 279 |
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-11 1746 ax-ext 2334 |
This theorem depends on definitions: df-bi 177 df-an 360 df-3an 936 df-ex 1542 df-cleq 2346 df-clel 2349 df-sfin 4447 |
This theorem is referenced by: sfintfinlem1 4532 sfintfin 4533 spfinsfincl 4540 t1csfin1c 4546 vfinspss 4552 |
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