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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 2320 | . . 3 |
4 | eleq2 2234 | . . . 4 | |
5 | 4 | anbi1d 462 | . . 3 |
6 | 3, 5 | mobid 2054 | . 2 |
7 | df-rmo 2456 | . 2 | |
8 | df-rmo 2456 | . 2 | |
9 | 6, 7, 8 | 3bitr4g 222 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wceq 1348 wmo 2020 wcel 2141 wnfc 2299 wrmo 2451 |
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 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-ext 2152 |
This theorem depends on definitions: df-bi 116 df-tru 1351 df-nf 1454 df-sb 1756 df-eu 2022 df-mo 2023 df-cleq 2163 df-clel 2166 df-nfc 2301 df-rmo 2456 |
This theorem is referenced by: rmoeq1 2668 |
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