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Mirrors > Home > MPE Home > Th. List > csbopab | Structured version Visualization version Unicode version |
Description: Move substitution into a class abstraction. Version of csbopabgALT 4734 without a sethood antecedent but depending on more axioms. (Contributed by NM, 6-Aug-2007.) (Revised by NM, 23-Aug-2018.) |
Ref | Expression |
---|---|
csbopab |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | csbeq1 3352 |
. . . 4
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2 | dfsbcq2 3258 |
. . . . 5
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3 | 2 | opabbidv 4459 |
. . . 4
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4 | 1, 3 | eqeq12d 2486 |
. . 3
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5 | vex 3034 |
. . . 4
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6 | nfs1v 2286 |
. . . . 5
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7 | 6 | nfopab 4461 |
. . . 4
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8 | sbequ12 2098 |
. . . . 5
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9 | 8 | opabbidv 4459 |
. . . 4
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10 | 5, 7, 9 | csbief 3374 |
. . 3
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11 | 4, 10 | vtoclg 3093 |
. 2
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12 | csbprc 3774 |
. . 3
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13 | sbcex 3265 |
. . . . . . 7
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14 | 13 | con3i 142 |
. . . . . 6
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15 | 14 | nexdv 1790 |
. . . . 5
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16 | 15 | nexdv 1790 |
. . . 4
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17 | opabn0 4732 |
. . . . 5
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18 | 17 | necon1bbii 2692 |
. . . 4
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19 | 16, 18 | sylib 201 |
. . 3
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20 | 12, 19 | eqtr4d 2508 |
. 2
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21 | 11, 20 | 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 1677 ax-4 1690 ax-5 1766 ax-6 1813 ax-7 1859 ax-9 1913 ax-10 1932 ax-11 1937 ax-12 1950 ax-13 2104 ax-ext 2451 ax-sep 4518 ax-nul 4527 ax-pr 4639 |
This theorem depends on definitions: df-bi 190 df-or 377 df-an 378 df-3an 1009 df-tru 1455 df-fal 1458 df-ex 1672 df-nf 1676 df-sb 1806 df-clab 2458 df-cleq 2464 df-clel 2467 df-nfc 2601 df-ne 2643 df-ral 2761 df-rab 2765 df-v 3033 df-sbc 3256 df-csb 3350 df-dif 3393 df-un 3395 df-in 3397 df-ss 3404 df-nul 3723 df-if 3873 df-sn 3960 df-pr 3962 df-op 3966 df-opab 4455 |
This theorem is referenced by: csbmpt12 4735 csbcnv 5023 |
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