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Mirrors > Home > ILE Home > Th. List > rabid2 | Unicode version |
Description: An "identity" law for restricted class abstraction. (Contributed by NM, 9-Oct-2003.) (Proof shortened by Andrew Salmon, 30-May-2011.) |
Ref | Expression |
---|---|
rabid2 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | abeq2 2298 |
. . 3
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2 | pm4.71 389 |
. . . 4
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3 | 2 | albii 1481 |
. . 3
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4 | 1, 3 | bitr4i 187 |
. 2
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5 | df-rab 2477 |
. . 3
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6 | 5 | eqeq2i 2200 |
. 2
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7 | df-ral 2473 |
. 2
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8 | 4, 6, 7 | 3bitr4i 212 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-5 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-11 1517 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 ax-ext 2171 |
This theorem depends on definitions: df-bi 117 df-nf 1472 df-sb 1774 df-clab 2176 df-cleq 2182 df-clel 2185 df-ral 2473 df-rab 2477 |
This theorem is referenced by: rabxmdc 3474 rabrsndc 3682 class2seteq 4188 dmmptg 5151 dmmptd 5372 fneqeql 5654 fmpt 5696 acexmidlemph 5899 inffiexmid 6949 ssfirab 6977 exmidaclem 7254 ioomax 10000 iccmax 10001 dfphi2 12332 phiprmpw 12334 phisum 12352 unennn 12528 znnen 12529 isnsg4 13255 lssuni 13823 |
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