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Theorem structfun 11759
 Description: Convert between two kinds of structure closure. (Contributed by Mario Carneiro, 29-Aug-2015.) (Proof shortened by AV, 12-Nov-2021.)
Hypothesis
Ref Expression
structfun.1 𝐹 Struct 𝑋
Assertion
Ref Expression
structfun Fun 𝐹

Proof of Theorem structfun
StepHypRef Expression
1 structfun.1 . 2 𝐹 Struct 𝑋
2 structfung 11758 . 2 (𝐹 Struct 𝑋 → Fun 𝐹)
31, 2ax-mp 7 1 Fun 𝐹
 Colors of variables: wff set class Syntax hints:   class class class wbr 3875  ◡ccnv 4476  Fun wfun 5053   Struct cstr 11737 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 584  ax-in2 585  ax-io 671  ax-5 1391  ax-7 1392  ax-gen 1393  ax-ie1 1437  ax-ie2 1438  ax-8 1450  ax-10 1451  ax-11 1452  ax-i12 1453  ax-bndl 1454  ax-4 1455  ax-14 1460  ax-17 1474  ax-i9 1478  ax-ial 1482  ax-i5r 1483  ax-ext 2082  ax-sep 3986  ax-pow 4038  ax-pr 4069 This theorem depends on definitions:  df-bi 116  df-3an 932  df-tru 1302  df-fal 1305  df-nf 1405  df-sb 1704  df-eu 1963  df-mo 1964  df-clab 2087  df-cleq 2093  df-clel 2096  df-nfc 2229  df-ne 2268  df-ral 2380  df-rex 2381  df-rab 2384  df-v 2643  df-dif 3023  df-un 3025  df-in 3027  df-ss 3034  df-nul 3311  df-pw 3459  df-sn 3480  df-pr 3481  df-op 3483  df-uni 3684  df-br 3876  df-opab 3930  df-xp 4483  df-rel 4484  df-cnv 4485  df-co 4486  df-dm 4487  df-iota 5024  df-fun 5061  df-fv 5067  df-struct 11743 This theorem is referenced by:  structfn  11760  strslfv  11785
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