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Mirrors > Home > ILE Home > Th. List > r19.12 | Unicode version |
Description: Theorem 19.12 of [Margaris] p. 89 with restricted quantifiers. (Contributed by NM, 15-Oct-2003.) (Proof shortened by Andrew Salmon, 30-May-2011.) |
Ref | Expression |
---|---|
r19.12 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfcv 2312 | . . . 4 | |
2 | nfra1 2501 | . . . 4 | |
3 | 1, 2 | nfrexxy 2509 | . . 3 |
4 | ax-1 6 | . . 3 | |
5 | 3, 4 | ralrimi 2541 | . 2 |
6 | rsp 2517 | . . . . 5 | |
7 | 6 | com12 30 | . . . 4 |
8 | 7 | reximdv 2571 | . . 3 |
9 | 8 | ralimia 2531 | . 2 |
10 | 5, 9 | syl 14 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wcel 2141 wral 2448 wrex 2449 |
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 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-4 1503 ax-17 1519 ax-ial 1527 ax-i5r 1528 ax-ext 2152 |
This theorem depends on definitions: df-bi 116 df-tru 1351 df-nf 1454 df-cleq 2163 df-clel 2166 df-nfc 2301 df-ral 2453 df-rex 2454 |
This theorem is referenced by: iuniin 3883 |
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