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Mirrors > Home > MPE Home > Th. List > sbcnel12g | Structured version Visualization version Unicode version |
Description: Distribute proper substitution through negated membership. (Contributed by Andrew Salmon, 18-Jun-2011.) |
Ref | Expression |
---|---|
sbcnel12g |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sbcng 3307 |
. 2
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2 | df-nel 2624 |
. . 3
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3 | 2 | sbcbii 3322 |
. 2
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4 | df-nel 2624 |
. . 3
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5 | sbcel12 3771 |
. . 3
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6 | 4, 5 | xchbinxr 313 |
. 2
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7 | 1, 3, 6 | 3bitr4g 292 |
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 1668 ax-4 1681 ax-5 1757 ax-6 1804 ax-7 1850 ax-10 1914 ax-11 1919 ax-12 1932 ax-13 2090 ax-ext 2430 |
This theorem depends on definitions: df-bi 189 df-or 372 df-an 373 df-tru 1446 df-fal 1449 df-ex 1663 df-nf 1667 df-sb 1797 df-clab 2437 df-cleq 2443 df-clel 2446 df-nfc 2580 df-nel 2624 df-v 3046 df-sbc 3267 df-csb 3363 df-dif 3406 df-in 3410 df-ss 3417 df-nul 3731 |
This theorem is referenced by: rusbcALT 36784 |
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