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Mirrors > Home > NFE Home > Th. List > iotacl | Unicode version |
Description: Membership law for
descriptions.
This can useful for expanding an unbounded iota-based definition (see df-iota 4340). If you have a bounded iota-based definition, riotacl2 in set.mm may be useful. (Contributed by Andrew Salmon, 1-Aug-2011.) |
Ref | Expression |
---|---|
iotacl |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | iota4 4358 |
. 2
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2 | df-sbc 3048 |
. 2
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3 | 1, 2 | sylib 188 |
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-nan 1288 df-tru 1319 df-ex 1542 df-nf 1545 df-sb 1649 df-eu 2208 df-clab 2340 df-cleq 2346 df-clel 2349 df-nfc 2479 df-rex 2621 df-v 2862 df-sbc 3048 df-nin 3212 df-compl 3213 df-un 3215 df-sn 3742 df-pr 3743 df-uni 3893 df-iota 4340 |
This theorem is referenced by: reiotacl2 4364 |
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