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Mirrors > Home > MPE Home > Th. List > rab0 | Structured version Unicode version |
Description: Any restricted class abstraction restricted to the empty set is empty. (Contributed by NM, 15-Oct-2003.) (Proof shortened by Andrew Salmon, 26-Jun-2011.) |
Ref | Expression |
---|---|
rab0 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | equid 1731 |
. . . . 5
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2 | noel 3742 |
. . . . . 6
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3 | 2 | intnanr 906 |
. . . . 5
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4 | 1, 3 | 2th 239 |
. . . 4
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5 | 4 | con2bii 332 |
. . 3
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6 | 5 | abbii 2585 |
. 2
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7 | df-rab 2804 |
. 2
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8 | dfnul2 3740 |
. 2
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9 | 6, 7, 8 | 3eqtr4i 2490 |
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 1952 ax-ext 2430 |
This theorem depends on definitions: df-bi 185 df-an 371 df-tru 1373 df-ex 1588 df-nf 1591 df-sb 1703 df-clab 2437 df-cleq 2443 df-clel 2446 df-nfc 2601 df-rab 2804 df-v 3073 df-dif 3432 df-nul 3739 |
This theorem is referenced by: rabsnif 4045 supp0 6798 scott0 8197 psgnfval 16117 pmtrsn 16136 00lsp 17177 rrgval 17473 usgra0v 23435 vdgr0 23715 |
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