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Mirrors > Home > MPE Home > Th. List > tskssel | Structured version Visualization version Unicode version |
Description: A part of a Tarski class strictly dominated by the class is an element of the class. JFM CLASSES2 th. 2. (Contributed by FL, 22-Feb-2011.) (Proof shortened by Mario Carneiro, 20-Sep-2014.) |
Ref | Expression |
---|---|
tskssel |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sdomnen 7984 | . . 3 | |
2 | 1 | 3ad2ant3 1084 | . 2 |
3 | tsken 9576 | . . . 4 | |
4 | 3 | 3adant3 1081 | . . 3 |
5 | 4 | ord 392 | . 2 |
6 | 2, 5 | mpd 15 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wn 3 wi 4 wo 383 w3a 1037 wcel 1990 wss 3574 class class class wbr 4653 cen 7952 csdm 7954 ctsk 9570 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 ax-sep 4781 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-3an 1039 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-ral 2917 df-rex 2918 df-rab 2921 df-v 3202 df-dif 3577 df-un 3579 df-in 3581 df-ss 3588 df-nul 3916 df-if 4087 df-pw 4160 df-sn 4178 df-pr 4180 df-op 4184 df-br 4654 df-sdom 7958 df-tsk 9571 |
This theorem is referenced by: tskpr 9592 tskwe2 9595 tskord 9602 tskcard 9603 tskurn 9611 |
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