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Mirrors > Home > ILE Home > Th. List > isotilem | Unicode version |
Description: Lemma for isoti 6894. (Contributed by Jim Kingdon, 26-Nov-2021.) |
Ref | Expression |
---|---|
isotilem |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | isof1o 5708 | . . . . . 6 | |
2 | f1of 5367 | . . . . . 6 | |
3 | ffvelrn 5553 | . . . . . . . 8 | |
4 | 3 | ex 114 | . . . . . . 7 |
5 | ffvelrn 5553 | . . . . . . . 8 | |
6 | 5 | ex 114 | . . . . . . 7 |
7 | 4, 6 | anim12d 333 | . . . . . 6 |
8 | 1, 2, 7 | 3syl 17 | . . . . 5 |
9 | 8 | imp 123 | . . . 4 |
10 | eqeq1 2146 | . . . . . 6 | |
11 | breq1 3932 | . . . . . . . 8 | |
12 | 11 | notbid 656 | . . . . . . 7 |
13 | breq2 3933 | . . . . . . . 8 | |
14 | 13 | notbid 656 | . . . . . . 7 |
15 | 12, 14 | anbi12d 464 | . . . . . 6 |
16 | 10, 15 | bibi12d 234 | . . . . 5 |
17 | eqeq2 2149 | . . . . . 6 | |
18 | breq2 3933 | . . . . . . . 8 | |
19 | 18 | notbid 656 | . . . . . . 7 |
20 | breq1 3932 | . . . . . . . 8 | |
21 | 20 | notbid 656 | . . . . . . 7 |
22 | 19, 21 | anbi12d 464 | . . . . . 6 |
23 | 17, 22 | bibi12d 234 | . . . . 5 |
24 | 16, 23 | rspc2v 2802 | . . . 4 |
25 | 9, 24 | syl 14 | . . 3 |
26 | f1of1 5366 | . . . . . . 7 | |
27 | 1, 26 | syl 14 | . . . . . 6 |
28 | f1fveq 5673 | . . . . . 6 | |
29 | 27, 28 | sylan 281 | . . . . 5 |
30 | 29 | bicomd 140 | . . . 4 |
31 | isorel 5709 | . . . . . 6 | |
32 | 31 | notbid 656 | . . . . 5 |
33 | isorel 5709 | . . . . . . 7 | |
34 | 33 | notbid 656 | . . . . . 6 |
35 | 34 | ancom2s 555 | . . . . 5 |
36 | 32, 35 | anbi12d 464 | . . . 4 |
37 | 30, 36 | bibi12d 234 | . . 3 |
38 | 25, 37 | sylibrd 168 | . 2 |
39 | 38 | ralrimdvva 2517 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wa 103 wb 104 wceq 1331 wcel 1480 wral 2416 class class class wbr 3929 wf 5119 wf1 5120 wf1o 5122 cfv 5123 wiso 5124 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-in1 603 ax-in2 604 ax-io 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-14 1492 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2121 ax-sep 4046 ax-pow 4098 ax-pr 4131 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-nf 1437 df-sb 1736 df-eu 2002 df-mo 2003 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-ral 2421 df-rex 2422 df-v 2688 df-sbc 2910 df-un 3075 df-in 3077 df-ss 3084 df-pw 3512 df-sn 3533 df-pr 3534 df-op 3536 df-uni 3737 df-br 3930 df-opab 3990 df-id 4215 df-xp 4545 df-rel 4546 df-cnv 4547 df-co 4548 df-dm 4549 df-rn 4550 df-iota 5088 df-fun 5125 df-fn 5126 df-f 5127 df-f1 5128 df-f1o 5130 df-fv 5131 df-isom 5132 |
This theorem is referenced by: isoti 6894 |
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