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Mirrors > Home > MPE Home > Th. List > cncfrss2 | Structured version Visualization version Unicode version |
Description: Reverse closure of the continuous function predicate. (Contributed by Mario Carneiro, 25-Aug-2014.) |
Ref | Expression |
---|---|
cncfrss2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-cncf 22681 | . . 3 | |
2 | 1 | elmpt2cl2 6878 | . 2 |
3 | 2 | elpwid 4170 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wcel 1990 wral 2912 wrex 2913 crab 2916 wss 3574 cpw 4158 class class class wbr 4653 cfv 5888 (class class class)co 6650 cmap 7857 cc 9934 clt 10074 cmin 10266 crp 11832 cabs 13974 ccncf 22679 |
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-8 1992 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 ax-sep 4781 ax-nul 4789 ax-pow 4843 ax-pr 4906 |
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-eu 2474 df-mo 2475 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-ne 2795 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-uni 4437 df-br 4654 df-opab 4713 df-xp 5120 df-dm 5124 df-iota 5851 df-fv 5896 df-ov 6653 df-oprab 6654 df-mpt2 6655 df-cncf 22681 |
This theorem is referenced by: cncff 22696 cncfi 22697 rescncf 22700 climcncf 22703 cncfco 22710 cncfcnvcn 22724 cnlimci 23653 cncfmptssg 40083 cncfcompt 40096 |
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