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Theorem structfun 11993
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 11992 . 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 3929  ccnv 4538  Fun wfun 5117   Struct cstr 11971
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 603  ax-in2 604  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-14 1492  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121  ax-sep 4046  ax-pow 4098  ax-pr 4131
This theorem depends on definitions:  df-bi 116  df-3an 964  df-tru 1334  df-fal 1337  df-nf 1437  df-sb 1736  df-eu 2002  df-mo 2003  df-clab 2126  df-cleq 2132  df-clel 2135  df-nfc 2270  df-ne 2309  df-ral 2421  df-rex 2422  df-rab 2425  df-v 2688  df-dif 3073  df-un 3075  df-in 3077  df-ss 3084  df-nul 3364  df-pw 3512  df-sn 3533  df-pr 3534  df-op 3536  df-uni 3737  df-br 3930  df-opab 3990  df-xp 4545  df-rel 4546  df-cnv 4547  df-co 4548  df-dm 4549  df-iota 5088  df-fun 5125  df-fv 5131  df-struct 11977
This theorem is referenced by:  structfn  11994  strslfv  12019
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