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Mirrors > Home > ILE Home > Th. List > fnmpti | Unicode version |
Description: Functionality and domain of an ordered-pair class abstraction. (Contributed by NM, 29-Jan-2004.) (Revised by Mario Carneiro, 31-Aug-2015.) |
Ref | Expression |
---|---|
fnmpti.1 | |
fnmpti.2 |
Ref | Expression |
---|---|
fnmpti |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | fnmpti.1 | . . 3 | |
2 | 1 | rgenw 2487 | . 2 |
3 | fnmpti.2 | . . 3 | |
4 | 3 | mptfng 5248 | . 2 |
5 | 2, 4 | mpbi 144 | 1 |
Colors of variables: wff set class |
Syntax hints: wceq 1331 wcel 1480 wral 2416 cvv 2686 cmpt 3989 wfn 5118 |
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-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-un 3075 df-in 3077 df-ss 3084 df-pw 3512 df-sn 3533 df-pr 3534 df-op 3536 df-br 3930 df-opab 3990 df-mpt 3991 df-id 4215 df-xp 4545 df-rel 4546 df-cnv 4547 df-co 4548 df-dm 4549 df-fun 5125 df-fn 5126 |
This theorem is referenced by: dmmpti 5252 fconst 5318 eufnfv 5648 idref 5658 fo1st 6055 fo2nd 6056 reldm 6084 oafnex 6340 fnoei 6348 oeiexg 6349 mapsnf1o2 6590 slotslfn 11985 topnfn 12125 fncld 12267 xmetunirn 12527 |
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