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Theorem mptrel 27713
 Description: The maps-to notation always describes a relationship. (Contributed by Scott Fenton, 16-Apr-2012.)
Assertion
Ref Expression
mptrel

Proof of Theorem mptrel
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 df-mpt 4450 . 2
21relopabi 5063 1
 Colors of variables: wff setvar class Syntax hints:   wa 369   wceq 1370   wcel 1758   cmpt 4448   wrel 4943 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603  ax-5 1671  ax-6 1710  ax-7 1730  ax-9 1762  ax-10 1777  ax-11 1782  ax-12 1794  ax-13 1952  ax-ext 2430  ax-sep 4511  ax-nul 4519  ax-pr 4629 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 967  df-tru 1373  df-ex 1588  df-nf 1591  df-sb 1703  df-clab 2437  df-cleq 2443  df-clel 2446  df-nfc 2601  df-ne 2646  df-ral 2800  df-rex 2801  df-rab 2804  df-v 3070  df-dif 3429  df-un 3431  df-in 3433  df-ss 3440  df-nul 3736  df-if 3890  df-sn 3976  df-pr 3978  df-op 3982  df-opab 4449  df-mpt 4450  df-xp 4944  df-rel 4945 This theorem is referenced by:  dfbigcup2  28064  imageval  28095
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