Theorem reldmmap 6551

Description: Set exponentiation is a well-behaved binary operator. (Contributed by Stefan O'Rear, 27-Feb-2015.)

Assertion

Ref	Expression
reldmmap	|- Rel dom ^m

Proof of Theorem reldmmap

Dummy variables x f y are mutually distinct and distinct from all other variables.

Step	Hyp	Ref	Expression
1		df-map 6544	. 2 |- ^m = ( x e. _V , y e. _V |-> { f | f : y --> x } )
2	1	reldmmpo 5882	1 |- Rel dom ^m

Syntax hints:   {cab 2125   _Vcvv 2686   dom cdm 4539   Rel wrel 4544   -->wf 5119   ^m cmap 6542

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 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-14 1492  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121  ax-sep 4046  ax-pow 4098  ax-pr 4131

This theorem depends on definitions:  df-bi 116  df-3an 964  df-tru 1334  df-nf 1437  df-sb 1736  df-eu 2002  df-mo 2003  df-clab 2126  df-cleq 2132  df-clel 2135  df-nfc 2270  df-ral 2421  df-rex 2422  df-v 2688  df-un 3075  df-in 3077  df-ss 3084  df-pw 3512  df-sn 3533  df-pr 3534  df-op 3536  df-br 3930  df-opab 3990  df-xp 4545  df-rel 4546  df-dm 4549  df-oprab 5778  df-mpo 5779  df-map 6544

This theorem is referenced by: (None)