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Mirrors > Home > ILE Home > Th. List > cleqf | Unicode version |
Description: Establish equality between classes, using bound-variable hypotheses instead of distinct variable conditions. See also cleqh 2289. (Contributed by NM, 5-Aug-1993.) (Revised by Mario Carneiro, 7-Oct-2016.) |
Ref | Expression |
---|---|
cleqf.1 |
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cleqf.2 |
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Ref | Expression |
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cleqf |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dfcleq 2183 |
. 2
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2 | nfv 1539 |
. . 3
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3 | cleqf.1 |
. . . . 5
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4 | 3 | nfcri 2326 |
. . . 4
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5 | cleqf.2 |
. . . . 5
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6 | 5 | nfcri 2326 |
. . . 4
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7 | 4, 6 | nfbi 1600 |
. . 3
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8 | eleq1 2252 |
. . . 4
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9 | eleq1 2252 |
. . . 4
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10 | 8, 9 | bibi12d 235 |
. . 3
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11 | 2, 7, 10 | cbval 1765 |
. 2
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12 | 1, 11 | bitr4i 187 |
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-io 710 ax-5 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-10 1516 ax-11 1517 ax-i12 1518 ax-bndl 1520 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-tru 1367 df-nf 1472 df-sb 1774 df-cleq 2182 df-clel 2185 df-nfc 2321 |
This theorem is referenced by: abid2f 2358 n0rf 3450 eq0 3456 iunab 3948 iinab 3963 sniota 5226 |
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