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Theorem elmapex 6611
 Description: Eliminate antecedent for mapping theorems: domain can be taken to be a set. (Contributed by Stefan O'Rear, 8-Oct-2014.)
Assertion
Ref Expression
elmapex

Proof of Theorem elmapex
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 df-map 6592 . 2
21elmpocl 6015 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 103   wcel 2128  cab 2143  cvv 2712  wf 5165  (class class class)co 5821   cmap 6590 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-uni 3773  df-br 3966  df-opab 4026  df-id 4253  df-xp 4591  df-rel 4592  df-cnv 4593  df-co 4594  df-dm 4595  df-iota 5134  df-fun 5171  df-fv 5177  df-ov 5824  df-oprab 5825  df-mpo 5826  df-map 6592 This theorem is referenced by:  elmapi  6612  elmapssres  6615  mapsspm  6624  mapss  6633
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