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Mirrors > Home > MPE Home > Th. List > ello1 | Structured version Visualization version Unicode version |
Description: Elementhood in the set of eventually upper bounded functions. (Contributed by Mario Carneiro, 26-May-2016.) |
Ref | Expression |
---|---|
ello1 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dmeq 5324 | . . . . 5 | |
2 | 1 | ineq1d 3813 | . . . 4 |
3 | fveq1 6190 | . . . . 5 | |
4 | 3 | breq1d 4663 | . . . 4 |
5 | 2, 4 | raleqbidv 3152 | . . 3 |
6 | 5 | 2rexbidv 3057 | . 2 |
7 | df-lo1 14222 | . 2 | |
8 | 6, 7 | elrab2 3366 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wb 196 wa 384 wceq 1483 wcel 1990 wral 2912 wrex 2913 cin 3573 class class class wbr 4653 cdm 5114 cfv 5888 (class class class)co 6650 cpm 7858 cr 9935 cpnf 10071 cle 10075 cico 12177 clo1 14218 |
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-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-sn 4178 df-pr 4180 df-op 4184 df-uni 4437 df-br 4654 df-dm 5124 df-iota 5851 df-fv 5896 df-lo1 14222 |
This theorem is referenced by: ello12 14247 lo1f 14249 lo1dm 14250 |
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