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Mirrors > Home > NFE Home > Th. List > sbcralg | Unicode version |
Description: Interchange class substitution and restricted quantifier. (Contributed by NM, 15-Nov-2005.) (Proof shortened by Andrew Salmon, 29-Jun-2011.) |
Ref | Expression |
---|---|
sbcralg |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dfsbcq2 3049 | . 2 | |
2 | dfsbcq2 3049 | . . 3 | |
3 | 2 | ralbidv 2634 | . 2 |
4 | nfcv 2489 | . . . 4 | |
5 | nfs1v 2106 | . . . 4 | |
6 | 4, 5 | nfral 2667 | . . 3 |
7 | sbequ12 1919 | . . . 4 | |
8 | 7 | ralbidv 2634 | . . 3 |
9 | 6, 8 | sbie 2038 | . 2 |
10 | 1, 3, 9 | vtoclbg 2915 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 176 wceq 1642 wsb 1648 wcel 1710 wral 2614 wsbc 3046 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1546 ax-5 1557 ax-17 1616 ax-9 1654 ax-8 1675 ax-6 1729 ax-7 1734 ax-11 1746 ax-12 1925 ax-ext 2334 |
This theorem depends on definitions: df-bi 177 df-or 359 df-an 360 df-tru 1319 df-ex 1542 df-nf 1545 df-sb 1649 df-clab 2340 df-cleq 2346 df-clel 2349 df-nfc 2478 df-ral 2619 df-v 2861 df-sbc 3047 |
This theorem is referenced by: r19.12sn 3789 |
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