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Mirrors > Home > ILE Home > Th. List > sbccomlem | Unicode version |
Description: Lemma for sbccom 3053. (Contributed by NM, 14-Nov-2005.) (Revised by Mario Carneiro, 18-Oct-2016.) |
Ref | Expression |
---|---|
sbccomlem |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | excom 1675 |
. . . 4
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2 | exdistr 1921 |
. . . 4
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3 | an12 561 |
. . . . . . 7
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4 | 3 | exbii 1616 |
. . . . . 6
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5 | 19.42v 1918 |
. . . . . 6
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6 | 4, 5 | bitri 184 |
. . . . 5
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7 | 6 | exbii 1616 |
. . . 4
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8 | 1, 2, 7 | 3bitr3i 210 |
. . 3
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9 | sbc5 3001 |
. . 3
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10 | sbc5 3001 |
. . 3
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11 | 8, 9, 10 | 3bitr4i 212 |
. 2
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12 | sbc5 3001 |
. . 3
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13 | 12 | sbcbii 3037 |
. 2
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14 | sbc5 3001 |
. . 3
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15 | 14 | sbcbii 3037 |
. 2
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16 | 11, 13, 15 | 3bitr4i 212 |
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-v 2754 df-sbc 2978 |
This theorem is referenced by: sbccom 3053 |
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