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Mirrors > Home > ILE Home > Th. List > structfun | GIF version |
Description: Convert between two kinds of structure closure. (Contributed by Mario Carneiro, 29-Aug-2015.) (Proof shortened by AV, 12-Nov-2021.) |
Ref | Expression |
---|---|
structfun.1 | ⊢ 𝐹 Struct 𝑋 |
Ref | Expression |
---|---|
structfun | ⊢ Fun ◡◡𝐹 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | structfun.1 | . 2 ⊢ 𝐹 Struct 𝑋 | |
2 | structfung 12015 | . 2 ⊢ (𝐹 Struct 𝑋 → Fun ◡◡𝐹) | |
3 | 1, 2 | ax-mp 5 | 1 ⊢ Fun ◡◡𝐹 |
Colors of variables: wff set class |
Syntax hints: class class class wbr 3937 ◡ccnv 4546 Fun wfun 5125 Struct cstr 11994 |
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-fal 1338 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-ne 2310 df-ral 2422 df-rex 2423 df-rab 2426 df-v 2691 df-dif 3078 df-un 3080 df-in 3082 df-ss 3089 df-nul 3369 df-pw 3517 df-sn 3538 df-pr 3539 df-op 3541 df-uni 3745 df-br 3938 df-opab 3998 df-xp 4553 df-rel 4554 df-cnv 4555 df-co 4556 df-dm 4557 df-iota 5096 df-fun 5133 df-fv 5139 df-struct 12000 |
This theorem is referenced by: structfn 12017 strslfv 12042 |
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