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Mirrors > Home > ILE 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 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dfsbcq2 2857 |
. 2
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2 | dfsbcq2 2857 |
. . 3
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3 | 2 | ralbidv 2391 |
. 2
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4 | nfcv 2235 |
. . . 4
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5 | nfs1v 1870 |
. . . 4
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6 | 4, 5 | nfralxy 2425 |
. . 3
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7 | sbequ12 1708 |
. . . 4
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8 | 7 | ralbidv 2391 |
. . 3
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9 | 6, 8 | sbie 1728 |
. 2
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10 | 1, 3, 9 | vtoclbg 2694 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 668 ax-5 1388 ax-7 1389 ax-gen 1390 ax-ie1 1434 ax-ie2 1435 ax-8 1447 ax-10 1448 ax-11 1449 ax-i12 1450 ax-bndl 1451 ax-4 1452 ax-17 1471 ax-i9 1475 ax-ial 1479 ax-i5r 1480 ax-ext 2077 |
This theorem depends on definitions: df-bi 116 df-tru 1299 df-nf 1402 df-sb 1700 df-clab 2082 df-cleq 2088 df-clel 2091 df-nfc 2224 df-ral 2375 df-v 2635 df-sbc 2855 |
This theorem is referenced by: r19.12sn 3528 |
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