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Mirrors > Home > ILE Home > Th. List > supisoex | Unicode version |
Description: Lemma for supisoti 6905. (Contributed by Mario Carneiro, 24-Dec-2016.) |
Ref | Expression |
---|---|
supiso.1 | |
supiso.2 | |
supisoex.3 |
Ref | Expression |
---|---|
supisoex |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | supisoex.3 | . 2 | |
2 | supiso.1 | . . 3 | |
3 | supiso.2 | . . 3 | |
4 | simpl 108 | . . . . . 6 | |
5 | simpr 109 | . . . . . 6 | |
6 | 4, 5 | supisolem 6903 | . . . . 5 |
7 | isof1o 5716 | . . . . . . . 8 | |
8 | f1of 5375 | . . . . . . . 8 | |
9 | 4, 7, 8 | 3syl 17 | . . . . . . 7 |
10 | 9 | ffvelrnda 5563 | . . . . . 6 |
11 | breq1 3940 | . . . . . . . . . . 11 | |
12 | 11 | notbid 657 | . . . . . . . . . 10 |
13 | 12 | ralbidv 2438 | . . . . . . . . 9 |
14 | breq2 3941 | . . . . . . . . . . 11 | |
15 | 14 | imbi1d 230 | . . . . . . . . . 10 |
16 | 15 | ralbidv 2438 | . . . . . . . . 9 |
17 | 13, 16 | anbi12d 465 | . . . . . . . 8 |
18 | 17 | rspcev 2793 | . . . . . . 7 |
19 | 18 | ex 114 | . . . . . 6 |
20 | 10, 19 | syl 14 | . . . . 5 |
21 | 6, 20 | sylbid 149 | . . . 4 |
22 | 21 | rexlimdva 2552 | . . 3 |
23 | 2, 3, 22 | syl2anc 409 | . 2 |
24 | 1, 23 | mpd 13 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wa 103 wceq 1332 wcel 1481 wral 2417 wrex 2418 wss 3076 class class class wbr 3937 cima 4550 wf 5127 wf1o 5130 cfv 5131 wiso 5132 |
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 604 ax-in2 605 ax-io 699 ax-5 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-10 1484 ax-11 1485 ax-i12 1486 ax-bndl 1487 ax-4 1488 ax-14 1493 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 ax-ext 2122 ax-sep 4054 ax-pow 4106 ax-pr 4139 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1335 df-nf 1438 df-sb 1737 df-eu 2003 df-mo 2004 df-clab 2127 df-cleq 2133 df-clel 2136 df-nfc 2271 df-ral 2422 df-rex 2423 df-v 2691 df-sbc 2914 df-un 3080 df-in 3082 df-ss 3089 df-pw 3517 df-sn 3538 df-pr 3539 df-op 3541 df-uni 3745 df-br 3938 df-opab 3998 df-mpt 3999 df-id 4223 df-xp 4553 df-rel 4554 df-cnv 4555 df-co 4556 df-dm 4557 df-rn 4558 df-res 4559 df-ima 4560 df-iota 5096 df-fun 5133 df-fn 5134 df-f 5135 df-f1 5136 df-fo 5137 df-f1o 5138 df-fv 5139 df-isom 5140 |
This theorem is referenced by: (None) |
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