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Theorem structfun 12504
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 12503 . 2 (𝐹 Struct 𝑋 → Fun 𝐹)
31, 2ax-mp 5 1 Fun 𝐹
Colors of variables: wff set class
Syntax hints:   class class class wbr 4018  ccnv 4640  Fun wfun 5225   Struct cstr 12482
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-in1 615  ax-in2 616  ax-io 710  ax-5 1458  ax-7 1459  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-10 1516  ax-11 1517  ax-i12 1518  ax-bndl 1520  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-i5r 1546  ax-14 2163  ax-ext 2171  ax-sep 4136  ax-pow 4189  ax-pr 4224
This theorem depends on definitions:  df-bi 117  df-3an 982  df-tru 1367  df-fal 1370  df-nf 1472  df-sb 1774  df-eu 2041  df-mo 2042  df-clab 2176  df-cleq 2182  df-clel 2185  df-nfc 2321  df-ne 2361  df-ral 2473  df-rex 2474  df-rab 2477  df-v 2754  df-dif 3146  df-un 3148  df-in 3150  df-ss 3157  df-nul 3438  df-pw 3592  df-sn 3613  df-pr 3614  df-op 3616  df-uni 3825  df-br 4019  df-opab 4080  df-xp 4647  df-rel 4648  df-cnv 4649  df-co 4650  df-dm 4651  df-iota 5193  df-fun 5233  df-fv 5239  df-struct 12488
This theorem is referenced by:  structfn  12505  strslfv  12531
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