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Mirrors > Home > MPE Home > Th. List > cnfval | Structured version Visualization version Unicode version |
Description: The set of all continuous functions from topology to topology . (Contributed by NM, 17-Oct-2006.) (Revised by Mario Carneiro, 21-Aug-2015.) |
Ref | Expression |
---|---|
cnfval | TopOn TopOn |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-cn 21031 | . . 3 | |
2 | 1 | a1i 11 | . 2 TopOn TopOn |
3 | simprr 796 | . . . . . 6 TopOn TopOn | |
4 | 3 | unieqd 4446 | . . . . 5 TopOn TopOn |
5 | toponuni 20719 | . . . . . 6 TopOn | |
6 | 5 | ad2antlr 763 | . . . . 5 TopOn TopOn |
7 | 4, 6 | eqtr4d 2659 | . . . 4 TopOn TopOn |
8 | simprl 794 | . . . . . 6 TopOn TopOn | |
9 | 8 | unieqd 4446 | . . . . 5 TopOn TopOn |
10 | toponuni 20719 | . . . . . 6 TopOn | |
11 | 10 | ad2antrr 762 | . . . . 5 TopOn TopOn |
12 | 9, 11 | eqtr4d 2659 | . . . 4 TopOn TopOn |
13 | 7, 12 | oveq12d 6668 | . . 3 TopOn TopOn |
14 | 8 | eleq2d 2687 | . . . 4 TopOn TopOn |
15 | 3, 14 | raleqbidv 3152 | . . 3 TopOn TopOn |
16 | 13, 15 | rabeqbidv 3195 | . 2 TopOn TopOn |
17 | topontop 20718 | . . 3 TopOn | |
18 | 17 | adantr 481 | . 2 TopOn TopOn |
19 | topontop 20718 | . . 3 TopOn | |
20 | 19 | adantl 482 | . 2 TopOn TopOn |
21 | ovex 6678 | . . . 4 | |
22 | 21 | rabex 4813 | . . 3 |
23 | 22 | a1i 11 | . 2 TopOn TopOn |
24 | 2, 16, 18, 20, 23 | ovmpt2d 6788 | 1 TopOn TopOn |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wa 384 wceq 1483 wcel 1990 wral 2912 crab 2916 cvv 3200 cuni 4436 ccnv 5113 cima 5117 cfv 5888 (class class class)co 6650 cmpt2 6652 cmap 7857 ctop 20698 TopOnctopon 20715 ccn 21028 |
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 ax-un 6949 |
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-sbc 3436 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-mpt 4730 df-id 5024 df-xp 5120 df-rel 5121 df-cnv 5122 df-co 5123 df-dm 5124 df-iota 5851 df-fun 5890 df-fv 5896 df-ov 6653 df-oprab 6654 df-mpt2 6655 df-topon 20716 df-cn 21031 |
This theorem is referenced by: iscn 21039 cnfex 39187 |
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