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Mirrors > Home > ILE Home > Th. List > fpr | Unicode version |
Description: A function with a domain of two elements. (Contributed by Jeff Madsen, 20-Jun-2010.) (Proof shortened by Andrew Salmon, 22-Oct-2011.) |
Ref | Expression |
---|---|
fpr.1 | |
fpr.2 | |
fpr.3 | |
fpr.4 |
Ref | Expression |
---|---|
fpr |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | fpr.1 | . . . . . 6 | |
2 | fpr.2 | . . . . . 6 | |
3 | fpr.3 | . . . . . 6 | |
4 | fpr.4 | . . . . . 6 | |
5 | 1, 2, 3, 4 | funpr 5145 | . . . . 5 |
6 | 3, 4 | dmprop 4983 | . . . . 5 |
7 | 5, 6 | jctir 311 | . . . 4 |
8 | df-fn 5096 | . . . 4 | |
9 | 7, 8 | sylibr 133 | . . 3 |
10 | df-pr 3504 | . . . . . 6 | |
11 | 10 | rneqi 4737 | . . . . 5 |
12 | rnun 4917 | . . . . 5 | |
13 | 1 | rnsnop 4989 | . . . . . . 7 |
14 | 2 | rnsnop 4989 | . . . . . . 7 |
15 | 13, 14 | uneq12i 3198 | . . . . . 6 |
16 | df-pr 3504 | . . . . . 6 | |
17 | 15, 16 | eqtr4i 2141 | . . . . 5 |
18 | 11, 12, 17 | 3eqtri 2142 | . . . 4 |
19 | 18 | eqimssi 3123 | . . 3 |
20 | 9, 19 | jctir 311 | . 2 |
21 | df-f 5097 | . 2 | |
22 | 20, 21 | sylibr 133 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wceq 1316 wcel 1465 wne 2285 cvv 2660 cun 3039 wss 3041 csn 3497 cpr 3498 cop 3500 cdm 4509 crn 4510 wfun 5087 wfn 5088 wf 5089 |
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 588 ax-in2 589 ax-io 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-14 1477 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 ax-sep 4016 ax-pow 4068 ax-pr 4101 |
This theorem depends on definitions: df-bi 116 df-3an 949 df-tru 1319 df-fal 1322 df-nf 1422 df-sb 1721 df-eu 1980 df-mo 1981 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-ne 2286 df-ral 2398 df-rex 2399 df-v 2662 df-dif 3043 df-un 3045 df-in 3047 df-ss 3054 df-nul 3334 df-pw 3482 df-sn 3503 df-pr 3504 df-op 3506 df-br 3900 df-opab 3960 df-id 4185 df-xp 4515 df-rel 4516 df-cnv 4517 df-co 4518 df-dm 4519 df-rn 4520 df-fun 5095 df-fn 5096 df-f 5097 |
This theorem is referenced by: (None) |
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