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Mirrors > Home > ILE Home > Th. List > ceqsex | Unicode version |
Description: Elimination of an existential quantifier, using implicit substitution. (Contributed by NM, 2-Mar-1995.) (Revised by Mario Carneiro, 10-Oct-2016.) |
Ref | Expression |
---|---|
ceqsex.1 | |
ceqsex.2 | |
ceqsex.3 |
Ref | Expression |
---|---|
ceqsex |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ceqsex.1 | . . 3 | |
2 | ceqsex.3 | . . . 4 | |
3 | 2 | biimpa 294 | . . 3 |
4 | 1, 3 | exlimi 1573 | . 2 |
5 | 2 | biimprcd 159 | . . . 4 |
6 | 1, 5 | alrimi 1502 | . . 3 |
7 | ceqsex.2 | . . . 4 | |
8 | 7 | isseti 2694 | . . 3 |
9 | exintr 1613 | . . 3 | |
10 | 6, 8, 9 | mpisyl 1422 | . 2 |
11 | 4, 10 | impbii 125 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wal 1329 wceq 1331 wnf 1436 wex 1468 wcel 1480 cvv 2686 |
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-5 1423 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-ext 2121 |
This theorem depends on definitions: df-bi 116 df-nf 1437 df-sb 1736 df-clab 2126 df-cleq 2132 df-clel 2135 df-v 2688 |
This theorem is referenced by: ceqsexv 2725 ceqsex2 2726 |
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