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Mirrors > Home > MPE Home > Th. List > iscmp | Structured version Visualization version Unicode version |
Description: The predicate "is a compact topology". (Contributed by FL, 22-Dec-2008.) (Revised by Mario Carneiro, 11-Feb-2015.) |
Ref | Expression |
---|---|
iscmp.1 |
Ref | Expression |
---|---|
iscmp |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pweq 4161 | . . 3 | |
2 | unieq 4444 | . . . . . 6 | |
3 | iscmp.1 | . . . . . 6 | |
4 | 2, 3 | syl6eqr 2674 | . . . . 5 |
5 | 4 | eqeq1d 2624 | . . . 4 |
6 | 4 | eqeq1d 2624 | . . . . 5 |
7 | 6 | rexbidv 3052 | . . . 4 |
8 | 5, 7 | imbi12d 334 | . . 3 |
9 | 1, 8 | raleqbidv 3152 | . 2 |
10 | df-cmp 21190 | . 2 | |
11 | 9, 10 | elrab2 3366 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 196 wa 384 wceq 1483 wcel 1990 wral 2912 wrex 2913 cin 3573 cpw 4158 cuni 4436 cfn 7955 ctop 20698 ccmp 21189 |
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 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 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-in 3581 df-ss 3588 df-pw 4160 df-uni 4437 df-cmp 21190 |
This theorem is referenced by: cmpcov 21192 cncmp 21195 fincmp 21196 cmptop 21198 cmpsub 21203 tgcmp 21204 uncmp 21206 sscmp 21208 cmpfi 21211 comppfsc 21335 txcmp 21446 alexsubb 21850 alexsubALT 21855 cmpcref 29917 onsucsuccmpi 32442 limsucncmpi 32444 heibor 33620 |
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