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Mirrors > Home > MPE Home > Th. List > sbco2 | Structured version Visualization version Unicode version |
Description: A composition law for substitution. (Contributed by NM, 30-Jun-1994.) (Revised by Mario Carneiro, 6-Oct-2016.) (Proof shortened by Wolf Lammen, 17-Sep-2018.) |
Ref | Expression |
---|---|
sbco2.1 |
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Ref | Expression |
---|---|
sbco2 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sbequ12 2093 |
. . . 4
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2 | sbequ 2215 |
. . . 4
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3 | 1, 2 | bitr3d 263 |
. . 3
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4 | 3 | sps 1953 |
. 2
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5 | nfnae 2162 |
. . 3
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6 | sbco2.1 |
. . . 4
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7 | 6 | nfsb4 2229 |
. . 3
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8 | 2 | a1i 11 |
. . 3
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9 | 5, 7, 8 | sbied 2248 |
. 2
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10 | 4, 9 | pm2.61i 169 |
1
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Colors of variables: wff setvar class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1679 ax-4 1692 ax-5 1768 ax-6 1815 ax-7 1861 ax-10 1925 ax-11 1930 ax-12 1943 ax-13 2101 |
This theorem depends on definitions: df-bi 190 df-or 376 df-an 377 df-ex 1674 df-nf 1678 df-sb 1808 |
This theorem is referenced by: sbco2d 2255 equsb3ALT 2272 elsb3 2273 elsb4 2274 sb7f 2292 sbco4lem 2304 sbco4 2305 eqsb3 2566 clelsb3 2567 cbvab 2584 sbralie 3043 sbcco 3301 clelsb3f 28164 bj-clelsb3 31501 |
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