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Mirrors > Home > MPE Home > Th. List > sbccsb2 | Structured version Visualization version Unicode version |
Description: Substitution into a wff expressed in using substitution into a class. (Contributed by NM, 27-Nov-2005.) (Revised by NM, 18-Aug-2018.) |
Ref | Expression |
---|---|
sbccsb2 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sbcex 3244 |
. 2
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2 | elex 3021 |
. 2
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3 | abid 2439 |
. . . 4
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4 | 3 | sbcbii 3290 |
. . 3
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5 | sbcel12 3739 |
. . . 4
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6 | csbvarg 3759 |
. . . . 5
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7 | 6 | eleq1d 2513 |
. . . 4
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8 | 5, 7 | syl5bb 265 |
. . 3
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9 | 4, 8 | syl5bbr 267 |
. 2
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10 | 1, 2, 9 | pm5.21nii 359 |
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 1672 ax-4 1685 ax-5 1761 ax-6 1808 ax-7 1854 ax-10 1918 ax-11 1923 ax-12 1936 ax-13 2091 ax-ext 2431 |
This theorem depends on definitions: df-bi 190 df-or 376 df-an 377 df-tru 1450 df-fal 1453 df-ex 1667 df-nf 1671 df-sb 1801 df-clab 2438 df-cleq 2444 df-clel 2447 df-nfc 2581 df-v 3014 df-sbc 3235 df-csb 3331 df-dif 3374 df-in 3378 df-ss 3385 df-nul 3699 |
This theorem is referenced by: (None) |
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