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Theorem funmpt2 5267
Description: Functionality of a class given by a maps-to notation. (Contributed by FL, 17-Feb-2008.) (Revised by Mario Carneiro, 31-May-2014.)
Hypothesis
Ref Expression
funmpt2.1 𝐹 = (𝑥𝐴𝐵)
Assertion
Ref Expression
funmpt2 Fun 𝐹

Proof of Theorem funmpt2
StepHypRef Expression
1 funmpt 5266 . 2 Fun (𝑥𝐴𝐵)
2 funmpt2.1 . . 3 𝐹 = (𝑥𝐴𝐵)
32funeqi 5249 . 2 (Fun 𝐹 ↔ Fun (𝑥𝐴𝐵))
41, 3mpbir 146 1 Fun 𝐹
Colors of variables: wff set class
Syntax hints:   = wceq 1363  cmpt 4076  Fun wfun 5222
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-io 710  ax-5 1457  ax-7 1458  ax-gen 1459  ax-ie1 1503  ax-ie2 1504  ax-8 1514  ax-10 1515  ax-11 1516  ax-i12 1517  ax-bndl 1519  ax-4 1520  ax-17 1536  ax-i9 1540  ax-ial 1544  ax-i5r 1545  ax-14 2161  ax-ext 2169  ax-sep 4133  ax-pow 4186  ax-pr 4221
This theorem depends on definitions:  df-bi 117  df-3an 981  df-tru 1366  df-nf 1471  df-sb 1773  df-eu 2039  df-mo 2040  df-clab 2174  df-cleq 2180  df-clel 2183  df-nfc 2318  df-ral 2470  df-rex 2471  df-v 2751  df-un 3145  df-in 3147  df-ss 3154  df-pw 3589  df-sn 3610  df-pr 3611  df-op 3613  df-br 4016  df-opab 4077  df-mpt 4078  df-id 4305  df-xp 4644  df-rel 4645  df-cnv 4646  df-co 4647  df-fun 5230
This theorem is referenced by:  fvmptss2  5604  mptrcl  5611  elfvmptrab1  5623  frectfr  6415  frecsuclem  6421  caseinj  7102  caseinl  7104  caseinr  7105  omp1eomlem  7107  djudoml  7232  djudomr  7233  fihashf1rn  10782  lidlmex  13664  funtopon  13808  eltg4i  13851  eltg3  13853  tg1  13855  tg2  13856  tgclb  13861  lmrcl  13987  exmidsbthrlem  15067
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