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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 2237. (Contributed by NM, 5-Aug-1993.) (Revised by Mario Carneiro, 7-Oct-2016.) |
Ref | Expression |
---|---|
cleqf.1 | |
cleqf.2 |
Ref | Expression |
---|---|
cleqf |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dfcleq 2131 | . 2 | |
2 | nfv 1508 | . . 3 | |
3 | cleqf.1 | . . . . 5 | |
4 | 3 | nfcri 2273 | . . . 4 |
5 | cleqf.2 | . . . . 5 | |
6 | 5 | nfcri 2273 | . . . 4 |
7 | 4, 6 | nfbi 1568 | . . 3 |
8 | eleq1 2200 | . . . 4 | |
9 | eleq1 2200 | . . . 4 | |
10 | 8, 9 | bibi12d 234 | . . 3 |
11 | 2, 7, 10 | cbval 1727 | . 2 |
12 | 1, 11 | bitr4i 186 | 1 |
Colors of variables: wff set class |
Syntax hints: wb 104 wal 1329 wceq 1331 wcel 1480 wnfc 2266 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2119 |
This theorem depends on definitions: df-bi 116 df-tru 1334 df-nf 1437 df-sb 1736 df-cleq 2130 df-clel 2133 df-nfc 2268 |
This theorem is referenced by: abid2f 2304 n0rf 3370 eq0 3376 iunab 3854 iinab 3869 sniota 5110 |
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