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Mirrors > Home > MPE Home > Th. List > rabss2 | Structured version Unicode version |
Description: Subclass law for restricted abstraction. (Contributed by NM, 18-Dec-2004.) (Proof shortened by Andrew Salmon, 26-Jun-2011.) |
Ref | Expression |
---|---|
rabss2 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pm3.45 830 |
. . . 4
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2 | 1 | alimi 1605 |
. . 3
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3 | dfss2 3446 |
. . 3
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4 | ss2ab 3521 |
. . 3
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5 | 2, 3, 4 | 3imtr4i 266 |
. 2
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6 | df-rab 2804 |
. 2
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7 | df-rab 2804 |
. 2
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8 | 5, 6, 7 | 3sstr4g 3498 |
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 1592 ax-4 1603 ax-5 1671 ax-6 1710 ax-7 1730 ax-10 1777 ax-11 1782 ax-12 1794 ax-13 1952 ax-ext 2430 |
This theorem depends on definitions: df-bi 185 df-or 370 df-an 371 df-tru 1373 df-ex 1588 df-nf 1591 df-sb 1703 df-clab 2437 df-cleq 2443 df-clel 2446 df-nfc 2601 df-rab 2804 df-in 3436 df-ss 3443 |
This theorem is referenced by: sess2 4790 suppfnss 6817 hashbcss 14176 dprdss 16640 minveclem4 21044 prmdvdsfi 22571 mumul 22645 sqff1o 22646 rpvmasumlem 22862 shatomistici 25910 xpinpreima2 26475 ballotth 27057 rmxyelqirr 29392 idomodle 29702 clwwlknfi 30618 disjxwwlkn 30705 bj-unrab 32732 lssats 32966 lpssat 32967 lssatle 32969 lssat 32970 atlatmstc 33273 dochspss 35332 |
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