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Mirrors > Home > ILE Home > Th. List > dff3im | Unicode version |
Description: Property of a mapping. (Contributed by Jim Kingdon, 4-Jan-2019.) |
Ref | Expression |
---|---|
dff3im |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | fssxp 5349 | . 2 | |
2 | ffun 5334 | . . . . . . . 8 | |
3 | 2 | adantr 274 | . . . . . . 7 |
4 | fdm 5337 | . . . . . . . . 9 | |
5 | 4 | eleq2d 2234 | . . . . . . . 8 |
6 | 5 | biimpar 295 | . . . . . . 7 |
7 | funfvop 5591 | . . . . . . 7 | |
8 | 3, 6, 7 | syl2anc 409 | . . . . . 6 |
9 | df-br 3977 | . . . . . 6 | |
10 | 8, 9 | sylibr 133 | . . . . 5 |
11 | funfvex 5497 | . . . . . . 7 | |
12 | breq2 3980 | . . . . . . . 8 | |
13 | 12 | spcegv 2809 | . . . . . . 7 |
14 | 11, 13 | syl 14 | . . . . . 6 |
15 | 3, 6, 14 | syl2anc 409 | . . . . 5 |
16 | 10, 15 | mpd 13 | . . . 4 |
17 | funmo 5197 | . . . . . 6 | |
18 | 2, 17 | syl 14 | . . . . 5 |
19 | 18 | adantr 274 | . . . 4 |
20 | eu5 2060 | . . . 4 | |
21 | 16, 19, 20 | sylanbrc 414 | . . 3 |
22 | 21 | ralrimiva 2537 | . 2 |
23 | 1, 22 | jca 304 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wex 1479 weu 2013 wmo 2014 wcel 2135 wral 2442 cvv 2721 wss 3111 cop 3573 class class class wbr 3976 cxp 4596 cdm 4598 wfun 5176 wf 5178 cfv 5182 |
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 4094 ax-pow 4147 ax-pr 4181 |
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 2723 df-sbc 2947 df-un 3115 df-in 3117 df-ss 3124 df-pw 3555 df-sn 3576 df-pr 3577 df-op 3579 df-uni 3784 df-br 3977 df-opab 4038 df-id 4265 df-xp 4604 df-rel 4605 df-cnv 4606 df-co 4607 df-dm 4608 df-rn 4609 df-iota 5147 df-fun 5184 df-fn 5185 df-f 5186 df-fv 5190 |
This theorem is referenced by: dff4im 5625 |
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