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Mirrors > Home > ILE Home > Th. List > ceqsrexbv | Unicode version |
Description: Elimination of a restricted existential quantifier, using implicit substitution. (Contributed by Mario Carneiro, 14-Mar-2014.) |
Ref | Expression |
---|---|
ceqsrexv.1 |
Ref | Expression |
---|---|
ceqsrexbv |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | r19.42v 2614 | . 2 | |
2 | eleq1 2220 | . . . . . . 7 | |
3 | 2 | adantr 274 | . . . . . 6 |
4 | 3 | pm5.32ri 451 | . . . . 5 |
5 | 4 | bicomi 131 | . . . 4 |
6 | 5 | baib 905 | . . 3 |
7 | 6 | rexbiia 2472 | . 2 |
8 | ceqsrexv.1 | . . . 4 | |
9 | 8 | ceqsrexv 2842 | . . 3 |
10 | 9 | pm5.32i 450 | . 2 |
11 | 1, 7, 10 | 3bitr3i 209 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wceq 1335 wcel 2128 wrex 2436 |
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-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-rex 2441 df-v 2714 |
This theorem is referenced by: frecsuclem 6353 |
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