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Mirrors > Home > ILE Home > Th. List > sbcco | Unicode version |
Description: A composition law for class substitution. (Contributed by NM, 26-Sep-2003.) (Revised by Mario Carneiro, 13-Oct-2016.) |
Ref | Expression |
---|---|
sbcco |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sbcex 2994 |
. 2
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2 | sbcex 2994 |
. 2
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3 | dfsbcq 2987 |
. . 3
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4 | dfsbcq 2987 |
. . 3
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5 | sbsbc 2989 |
. . . . . 6
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6 | 5 | sbbii 1776 |
. . . . 5
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7 | nfv 1539 |
. . . . . 6
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8 | 7 | sbco2 1981 |
. . . . 5
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9 | sbsbc 2989 |
. . . . 5
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10 | 6, 8, 9 | 3bitr3ri 211 |
. . . 4
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11 | sbsbc 2989 |
. . . 4
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12 | 10, 11 | bitri 184 |
. . 3
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13 | 3, 4, 12 | vtoclbg 2821 |
. 2
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14 | 1, 2, 13 | pm5.21nii 705 |
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 2175 |
This theorem depends on definitions: df-bi 117 df-tru 1367 df-nf 1472 df-sb 1774 df-clab 2180 df-cleq 2186 df-clel 2189 df-nfc 2325 df-v 2762 df-sbc 2986 |
This theorem is referenced by: sbc7 3012 sbccom 3061 sbcralt 3062 sbcrext 3063 csbco 3090 |
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