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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 2971 |
. 2
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2 | exsimpl 1617 |
. . 3
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3 | isset 2743 |
. . 3
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4 | 2, 3 | sylibr 134 |
. 2
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5 | dfsbcq2 2965 |
. . 3
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6 | eqeq2 2187 |
. . . . 5
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7 | 6 | anbi1d 465 |
. . . 4
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8 | 7 | exbidv 1825 |
. . 3
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9 | sb5 1887 |
. . 3
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10 | 5, 8, 9 | vtoclbg 2798 |
. 2
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11 | 1, 4, 10 | pm5.21nii 704 |
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 709 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-ext 2159 |
This theorem depends on definitions: df-bi 117 df-tru 1356 df-nf 1461 df-sb 1763 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-v 2739 df-sbc 2963 |
This theorem is referenced by: sbc6g 2987 sbc7 2989 sbciegft 2993 sbccomlem 3037 csb2 3059 rexsns 3631 |
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