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Mirrors > Home > MPE Home > Th. List > Mathboxes > setrec2lem1 | Structured version Visualization version Unicode version |
Description: Lemma for setrec2 42442. The functional part of has the same values as . (Contributed by Emmett Weisz, 4-Mar-2021.) (New usage is discouraged.) |
Ref | Expression |
---|---|
setrec2lem1 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | fvres 6207 | . 2 | |
2 | dmres 5419 | . . . . . . 7 | |
3 | inss1 3833 | . . . . . . 7 | |
4 | 2, 3 | eqsstri 3635 | . . . . . 6 |
5 | 4 | sseli 3599 | . . . . 5 |
6 | 5 | con3i 150 | . . . 4 |
7 | ndmfv 6218 | . . . 4 | |
8 | 6, 7 | syl 17 | . . 3 |
9 | vex 3203 | . . . . . . 7 | |
10 | breq1 4656 | . . . . . . . 8 | |
11 | 10 | eubidv 2490 | . . . . . . 7 |
12 | 9, 11 | elab 3350 | . . . . . 6 |
13 | 12 | notbii 310 | . . . . 5 |
14 | 13 | biimpi 206 | . . . 4 |
15 | tz6.12-2 6182 | . . . 4 | |
16 | 14, 15 | syl 17 | . . 3 |
17 | 8, 16 | eqtr4d 2659 | . 2 |
18 | 1, 17 | pm2.61i 176 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wn 3 wceq 1483 wcel 1990 weu 2470 cab 2608 cin 3573 c0 3915 class class class wbr 4653 cdm 5114 cres 5116 cfv 5888 |
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-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-opab 4713 df-xp 5120 df-dm 5124 df-res 5126 df-iota 5851 df-fv 5896 |
This theorem is referenced by: setrec2 42442 |
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