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Theorem structfun 11677
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 11676 . 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 3867   `'ccnv 4466   Fun wfun 5043   Struct cstr 11655
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 582  ax-in2 583  ax-io 668  ax-5 1388  ax-7 1389  ax-gen 1390  ax-ie1 1434  ax-ie2 1435  ax-8 1447  ax-10 1448  ax-11 1449  ax-i12 1450  ax-bndl 1451  ax-4 1452  ax-14 1457  ax-17 1471  ax-i9 1475  ax-ial 1479  ax-i5r 1480  ax-ext 2077  ax-sep 3978  ax-pow 4030  ax-pr 4060
This theorem depends on definitions:  df-bi 116  df-3an 929  df-tru 1299  df-fal 1302  df-nf 1402  df-sb 1700  df-eu 1958  df-mo 1959  df-clab 2082  df-cleq 2088  df-clel 2091  df-nfc 2224  df-ne 2263  df-ral 2375  df-rex 2376  df-rab 2379  df-v 2635  df-dif 3015  df-un 3017  df-in 3019  df-ss 3026  df-nul 3303  df-pw 3451  df-sn 3472  df-pr 3473  df-op 3475  df-uni 3676  df-br 3868  df-opab 3922  df-xp 4473  df-rel 4474  df-cnv 4475  df-co 4476  df-dm 4477  df-iota 5014  df-fun 5051  df-fv 5057  df-struct 11661
This theorem is referenced by:  structfn  11678  strslfv  11703
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