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Mirrors > Home > ILE Home > Th. List > rmoeq1f | Unicode version |
Description: Equality theorem for restricted at-most-one 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 2307 | . . 3 |
4 | eleq2 2221 | . . . 4 | |
5 | 4 | anbi1d 461 | . . 3 |
6 | 3, 5 | mobid 2041 | . 2 |
7 | df-rmo 2443 | . 2 | |
8 | df-rmo 2443 | . 2 | |
9 | 6, 7, 8 | 3bitr4g 222 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wceq 1335 wmo 2007 wcel 2128 wnfc 2286 wrmo 2438 |
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 699 ax-5 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-10 1485 ax-11 1486 ax-i12 1487 ax-bndl 1489 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2139 |
This theorem depends on definitions: df-bi 116 df-tru 1338 df-nf 1441 df-sb 1743 df-eu 2009 df-mo 2010 df-cleq 2150 df-clel 2153 df-nfc 2288 df-rmo 2443 |
This theorem is referenced by: rmoeq1 2655 |
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