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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 2980 |
. 2
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2 | dfsbcq2 2980 |
. . 3
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3 | 2 | ralbidv 2490 |
. 2
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4 | nfcv 2332 |
. . . 4
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5 | nfs1v 1951 |
. . . 4
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6 | 4, 5 | nfralxy 2528 |
. . 3
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7 | sbequ12 1782 |
. . . 4
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8 | 7 | ralbidv 2490 |
. . 3
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9 | 6, 8 | sbie 1802 |
. 2
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10 | 1, 3, 9 | vtoclbg 2813 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-io 710 ax-5 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-10 1516 ax-11 1517 ax-i12 1518 ax-bndl 1520 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 ax-ext 2171 |
This theorem depends on definitions: df-bi 117 df-tru 1367 df-nf 1472 df-sb 1774 df-clab 2176 df-cleq 2182 df-clel 2185 df-nfc 2321 df-ral 2473 df-v 2754 df-sbc 2978 |
This theorem is referenced by: r19.12sn 3673 |
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