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Mirrors > Home > ILE Home > Th. List > ceqsrex2v | Unicode version |
Description: Elimination of a restricted existential quantifier, using implicit substitution. (Contributed by NM, 29-Oct-2005.) |
Ref | Expression |
---|---|
ceqsrex2v.1 | |
ceqsrex2v.2 |
Ref | Expression |
---|---|
ceqsrex2v |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | anass 398 | . . . . . 6 | |
2 | 1 | rexbii 2440 | . . . . 5 |
3 | r19.42v 2586 | . . . . 5 | |
4 | 2, 3 | bitri 183 | . . . 4 |
5 | 4 | rexbii 2440 | . . 3 |
6 | ceqsrex2v.1 | . . . . . 6 | |
7 | 6 | anbi2d 459 | . . . . 5 |
8 | 7 | rexbidv 2436 | . . . 4 |
9 | 8 | ceqsrexv 2810 | . . 3 |
10 | 5, 9 | syl5bb 191 | . 2 |
11 | ceqsrex2v.2 | . . 3 | |
12 | 11 | ceqsrexv 2810 | . 2 |
13 | 10, 12 | sylan9bb 457 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wceq 1331 wcel 1480 wrex 2415 |
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 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2119 |
This theorem depends on definitions: df-bi 116 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2124 df-cleq 2130 df-clel 2133 df-nfc 2268 df-rex 2420 df-v 2683 |
This theorem is referenced by: (None) |
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