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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 4339). 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 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | iota4 4357 | . 2 | |
2 | df-sbc 3047 | . 2 | |
3 | 1, 2 | sylib 188 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wcel 1710 weu 2204 cab 2339 wsbc 3046 cio 4337 |
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 2478 df-rex 2620 df-v 2861 df-sbc 3047 df-nin 3211 df-compl 3212 df-un 3214 df-sn 3741 df-pr 3742 df-uni 3892 df-iota 4339 |
This theorem is referenced by: reiotacl2 4363 |
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