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Mirrors > Home > MPE Home > Th. List > ofrval | Structured version Visualization version Unicode version |
Description: Exhibit a function relation at a point. (Contributed by Mario Carneiro, 28-Jul-2014.) |
Ref | Expression |
---|---|
offval.1 | |
offval.2 | |
offval.3 | |
offval.4 | |
offval.5 | |
ofval.6 | |
ofval.7 |
Ref | Expression |
---|---|
ofrval |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | offval.1 | . . . . . 6 | |
2 | offval.2 | . . . . . 6 | |
3 | offval.3 | . . . . . 6 | |
4 | offval.4 | . . . . . 6 | |
5 | offval.5 | . . . . . 6 | |
6 | eqidd 2623 | . . . . . 6 | |
7 | eqidd 2623 | . . . . . 6 | |
8 | 1, 2, 3, 4, 5, 6, 7 | ofrfval 6905 | . . . . 5 |
9 | 8 | biimpa 501 | . . . 4 |
10 | fveq2 6191 | . . . . . 6 | |
11 | fveq2 6191 | . . . . . 6 | |
12 | 10, 11 | breq12d 4666 | . . . . 5 |
13 | 12 | rspccv 3306 | . . . 4 |
14 | 9, 13 | syl 17 | . . 3 |
15 | 14 | 3impia 1261 | . 2 |
16 | simp1 1061 | . . 3 | |
17 | inss1 3833 | . . . . 5 | |
18 | 5, 17 | eqsstr3i 3636 | . . . 4 |
19 | simp3 1063 | . . . 4 | |
20 | 18, 19 | sseldi 3601 | . . 3 |
21 | ofval.6 | . . 3 | |
22 | 16, 20, 21 | syl2anc 693 | . 2 |
23 | inss2 3834 | . . . . 5 | |
24 | 5, 23 | eqsstr3i 3636 | . . . 4 |
25 | 24, 19 | sseldi 3601 | . . 3 |
26 | ofval.7 | . . 3 | |
27 | 16, 25, 26 | syl2anc 693 | . 2 |
28 | 15, 22, 27 | 3brtr3d 4684 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wa 384 w3a 1037 wceq 1483 wcel 1990 wral 2912 cin 3573 class class class wbr 4653 wfn 5883 cfv 5888 cofr 6896 |
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 ax-rep 4771 ax-sep 4781 ax-nul 4789 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-reu 2919 df-rab 2921 df-v 3202 df-sbc 3436 df-csb 3534 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-iun 4522 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-rn 5125 df-res 5126 df-ima 5127 df-iota 5851 df-fun 5890 df-fn 5891 df-f 5892 df-f1 5893 df-fo 5894 df-f1o 5895 df-fv 5896 df-ofr 6898 |
This theorem is referenced by: itg1le 23480 gsumle 29779 ftc1anclem5 33489 |
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