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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 2302 |
. . 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 2481 |
. . 3
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6 | 5 | eqeq2i 2204 |
. 2
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7 | df-ral 2477 |
. 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 2175 |
This theorem depends on definitions: df-bi 117 df-nf 1472 df-sb 1774 df-clab 2180 df-cleq 2186 df-clel 2189 df-ral 2477 df-rab 2481 |
This theorem is referenced by: rabxmdc 3478 rabrsndc 3686 class2seteq 4192 dmmptg 5163 dmmptd 5384 fneqeql 5666 fmpt 5708 acexmidlemph 5911 inffiexmid 6962 ssfirab 6990 exmidaclem 7268 ioomax 10014 iccmax 10015 dfphi2 12358 phiprmpw 12360 phisum 12378 unennn 12554 znnen 12555 isnsg4 13282 lssuni 13859 lgsquadlem2 15194 |
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