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Mirrors > Home > ILE Home > Th. List > sbc5 | Unicode version |
Description: An equivalence for class substitution. (Contributed by NM, 23-Aug-1993.) (Revised by Mario Carneiro, 12-Oct-2016.) |
Ref | Expression |
---|---|
sbc5 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sbcex 2862 |
. 2
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2 | exsimpl 1560 |
. . 3
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3 | isset 2639 |
. . 3
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4 | 2, 3 | sylibr 133 |
. 2
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5 | dfsbcq2 2857 |
. . 3
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6 | eqeq2 2104 |
. . . . 5
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7 | 6 | anbi1d 454 |
. . . 4
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8 | 7 | exbidv 1760 |
. . 3
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9 | sb5 1822 |
. . 3
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10 | 5, 8, 9 | vtoclbg 2694 |
. 2
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11 | 1, 4, 10 | pm5.21nii 658 |
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-v 2635 df-sbc 2855 |
This theorem is referenced by: sbc6g 2878 sbc7 2880 sbciegft 2883 sbccomlem 2927 csb2 2949 rexsns 3502 |
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