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Mirrors > Home > ILE Home > Th. List > fssxp | Unicode version |
Description: A mapping is a class of ordered pairs. (Contributed by NM, 3-Aug-1994.) (Proof shortened by Andrew Salmon, 17-Sep-2011.) |
Ref | Expression |
---|---|
fssxp |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | frel 5337 | . . 3 | |
2 | relssdmrn 5119 | . . 3 | |
3 | 1, 2 | syl 14 | . 2 |
4 | fdm 5338 | . . . 4 | |
5 | eqimss 3192 | . . . 4 | |
6 | 4, 5 | syl 14 | . . 3 |
7 | frn 5341 | . . 3 | |
8 | xpss12 4706 | . . 3 | |
9 | 6, 7, 8 | syl2anc 409 | . 2 |
10 | 3, 9 | sstrd 3148 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1342 wss 3112 cxp 4597 cdm 4599 crn 4600 wrel 4604 wf 5179 |
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 699 ax-5 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-10 1492 ax-11 1493 ax-i12 1494 ax-bndl 1496 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 ax-14 2138 ax-ext 2146 ax-sep 4095 ax-pow 4148 ax-pr 4182 |
This theorem depends on definitions: df-bi 116 df-3an 969 df-tru 1345 df-nf 1448 df-sb 1750 df-eu 2016 df-mo 2017 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-ral 2447 df-rex 2448 df-v 2724 df-un 3116 df-in 3118 df-ss 3125 df-pw 3556 df-sn 3577 df-pr 3578 df-op 3580 df-br 3978 df-opab 4039 df-xp 4605 df-rel 4606 df-cnv 4607 df-dm 4609 df-rn 4610 df-fun 5185 df-fn 5186 df-f 5187 |
This theorem is referenced by: fex2 5351 funssxp 5352 opelf 5354 fabexg 5370 dff2 5624 dff3im 5625 f2ndf 6186 f1o2ndf1 6188 tfrlemibfn 6288 tfr1onlembfn 6304 tfrcllembfn 6317 mapex 6612 uniixp 6679 ixxex 9827 pw1nct 13735 |
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