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Theorem funmpt2 5209
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 5208 . 2 Fun (𝑥𝐴𝐵)
2 funmpt2.1 . . 3 𝐹 = (𝑥𝐴𝐵)
32funeqi 5191 . 2 (Fun 𝐹 ↔ Fun (𝑥𝐴𝐵))
41, 3mpbir 145 1 Fun 𝐹
Colors of variables: wff set class
Syntax hints:   = wceq 1335  cmpt 4025  Fun wfun 5164
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-io 699  ax-5 1427  ax-7 1428  ax-gen 1429  ax-ie1 1473  ax-ie2 1474  ax-8 1484  ax-10 1485  ax-11 1486  ax-i12 1487  ax-bndl 1489  ax-4 1490  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-14 2131  ax-ext 2139  ax-sep 4082  ax-pow 4135  ax-pr 4169
This theorem depends on definitions:  df-bi 116  df-3an 965  df-tru 1338  df-nf 1441  df-sb 1743  df-eu 2009  df-mo 2010  df-clab 2144  df-cleq 2150  df-clel 2153  df-nfc 2288  df-ral 2440  df-rex 2441  df-v 2714  df-un 3106  df-in 3108  df-ss 3115  df-pw 3545  df-sn 3566  df-pr 3567  df-op 3569  df-br 3966  df-opab 4026  df-mpt 4027  df-id 4253  df-xp 4592  df-rel 4593  df-cnv 4594  df-co 4595  df-fun 5172
This theorem is referenced by:  fvmptss2  5543  mptrcl  5550  elfvmptrab1  5562  frectfr  6347  frecsuclem  6353  caseinj  7033  caseinl  7035  caseinr  7036  omp1eomlem  7038  djudoml  7154  djudomr  7155  fihashf1rn  10663  funtopon  12421  eltg4i  12466  eltg3  12468  tg1  12470  tg2  12471  tgclb  12476  lmrcl  12602  exmidsbthrlem  13604
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