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Mirrors > Home > ILE Home > Th. List > rspsbc | Unicode version |
Description: Restricted quantifier version of Axiom 4 of [Mendelson] p. 69. This provides an axiom for a predicate calculus for a restricted domain. This theorem generalizes the unrestricted stdpc4 1658 and spsbc 2775. See also rspsbca 2841 and rspcsbela . (Contributed by NM, 17-Nov-2006.) (Proof shortened by Mario Carneiro, 13-Oct-2016.) |
Ref | Expression |
---|---|
rspsbc |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cbvralsv 2544 | . 2 | |
2 | dfsbcq2 2767 | . . 3 | |
3 | 2 | rspcv 2652 | . 2 |
4 | 1, 3 | syl5bi 141 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wcel 1393 wsb 1645 wral 2306 wsbc 2764 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 ax-4 1400 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 |
This theorem depends on definitions: df-bi 110 df-tru 1246 df-nf 1350 df-sb 1646 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-ral 2311 df-v 2559 df-sbc 2765 |
This theorem is referenced by: rspsbca 2841 sbcth2 2845 rspcsbela 2905 riota5f 5492 riotass2 5494 fzrevral 8967 |
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