![]() |
Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
Mirrors > Home > MPE Home > Th. List > reueq1f | Unicode version |
Description: Equality theorem for restricted uniqueness quantifier, with bound-variable hypotheses instead of distinct variable restrictions. (Contributed by NM, 5-Apr-2004.) (Revised by Andrew Salmon, 11-Jul-2011.) |
Ref | Expression |
---|---|
raleq1f.1 | |
raleq1f.2 |
Ref | Expression |
---|---|
reueq1f |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | raleq1f.1 | . . . 4 | |
2 | raleq1f.2 | . . . 4 | |
3 | 1, 2 | nfeq 2630 | . . 3 |
4 | eleq2 2530 | . . . 4 | |
5 | 4 | anbi1d 704 | . . 3 |
6 | 3, 5 | eubid 2302 | . 2 |
7 | df-reu 2814 | . 2 | |
8 | df-reu 2814 | . 2 | |
9 | 6, 7, 8 | 3bitr4g 288 | 1 |
Colors of variables: wff setvar class |
Syntax hints: -> wi 4 <-> wb 184
/\ wa 369 = wceq 1395 e. wcel 1818
E! weu 2282 F/_ wnfc 2605 E! wreu 2809 |
This theorem is referenced by: reueq1 3056 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1618 ax-4 1631 ax-5 1704 ax-6 1747 ax-7 1790 ax-10 1837 ax-11 1842 ax-12 1854 ax-ext 2435 |
This theorem depends on definitions: df-bi 185 df-an 371 df-tru 1398 df-ex 1613 df-nf 1617 df-eu 2286 df-cleq 2449 df-clel 2452 df-nfc 2607 df-reu 2814 |
Copyright terms: Public domain | W3C validator |