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Mirrors > Home > ILE Home > Th. List > rmoeq1f | Unicode version |
Description: Equality theorem for restricted uniqueness quantifier, with bound-variable hypotheses instead of distinct variable restrictions. (Contributed by Alexander van der Vekens, 17-Jun-2017.) |
Ref | Expression |
---|---|
raleq1f.1 | |
raleq1f.2 |
Ref | Expression |
---|---|
rmoeq1f |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | raleq1f.1 | . . . 4 | |
2 | raleq1f.2 | . . . 4 | |
3 | 1, 2 | nfeq 2226 | . . 3 |
4 | eleq2 2142 | . . . 4 | |
5 | 4 | anbi1d 452 | . . 3 |
6 | 3, 5 | mobid 1976 | . 2 |
7 | df-rmo 2356 | . 2 | |
8 | df-rmo 2356 | . 2 | |
9 | 6, 7, 8 | 3bitr4g 221 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 102 wb 103 wceq 1284 wcel 1433 wmo 1942 wnfc 2206 wrmo 2351 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-io 662 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-10 1436 ax-11 1437 ax-i12 1438 ax-bndl 1439 ax-4 1440 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 |
This theorem depends on definitions: df-bi 115 df-tru 1287 df-nf 1390 df-sb 1686 df-eu 1944 df-mo 1945 df-cleq 2074 df-clel 2077 df-nfc 2208 df-rmo 2356 |
This theorem is referenced by: rmoeq1 2552 |
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