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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 1762 and spsbc 2960. See also rspsbca 3032 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 2706 | . 2 | |
2 | dfsbcq2 2952 | . . 3 | |
3 | 2 | rspcv 2824 | . 2 |
4 | 1, 3 | syl5bi 151 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wsb 1749 wcel 2135 wral 2442 wsbc 2949 |
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 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-10 1492 ax-11 1493 ax-i12 1494 ax-bndl 1496 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 ax-ext 2146 |
This theorem depends on definitions: df-bi 116 df-tru 1345 df-nf 1448 df-sb 1750 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-ral 2447 df-v 2726 df-sbc 2950 |
This theorem is referenced by: rspsbca 3032 sbcth2 3036 rspcsbela 3102 riota5f 5819 riotass2 5821 fzrevral 10034 fprodcllemf 11548 ctiunctlemf 12365 |
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