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Mirrors > Home > MPE Home > Th. List > sbccsb | Structured version Unicode version |
Description: Substitution into a wff expressed in terms of substitution into a class. (Contributed by NM, 15-Aug-2007.) (Revised by NM, 18-Aug-2018.) |
Ref | Expression |
---|---|
sbccsb |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | abid 2441 |
. . 3
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2 | 1 | sbcbii 3354 |
. 2
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3 | sbcel2 3792 |
. 2
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4 | 2, 3 | bitr3i 251 |
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 1592 ax-4 1603 ax-5 1671 ax-6 1710 ax-7 1730 ax-10 1777 ax-11 1782 ax-12 1794 ax-13 1955 ax-ext 2432 |
This theorem depends on definitions: df-bi 185 df-or 370 df-an 371 df-tru 1373 df-fal 1376 df-ex 1588 df-nf 1591 df-sb 1703 df-clab 2440 df-cleq 2446 df-clel 2449 df-nfc 2604 df-v 3080 df-sbc 3295 df-csb 3397 df-dif 3440 df-in 3444 df-ss 3451 df-nul 3747 |
This theorem is referenced by: (None) |
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