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Mirrors > Home > MPE Home > Th. List > csbsng | Structured version Visualization version Unicode version |
Description: Distribute proper substitution through the singleton of a class. csbsng 4030 is derived from the virtual deduction proof csbsngVD 37290. (Contributed by Alan Sare, 10-Nov-2012.) |
Ref | Expression |
---|---|
csbsng |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | csbab 3797 |
. . 3
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2 | sbceq2g 3779 |
. . . 4
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3 | 2 | abbidv 2569 |
. . 3
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4 | 1, 3 | syl5eq 2497 |
. 2
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5 | df-sn 3969 |
. . 3
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6 | 5 | csbeq2i 3782 |
. 2
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7 | df-sn 3969 |
. 2
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8 | 4, 6, 7 | 3eqtr4g 2510 |
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 1669 ax-4 1682 ax-5 1758 ax-6 1805 ax-7 1851 ax-10 1915 ax-11 1920 ax-12 1933 ax-13 2091 ax-ext 2431 |
This theorem depends on definitions: df-bi 189 df-or 372 df-an 373 df-tru 1447 df-fal 1450 df-ex 1664 df-nf 1668 df-sb 1798 df-clab 2438 df-cleq 2444 df-clel 2447 df-nfc 2581 df-v 3047 df-sbc 3268 df-csb 3364 df-dif 3407 df-in 3411 df-ss 3418 df-nul 3732 df-sn 3969 |
This theorem is referenced by: csbprg 4031 csbopg2 31725 csbpredg 31727 csbfv12gALTOLD 37213 csbfv12gALTVD 37296 |
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