Theorem nfmpo2 5839

Description: Bound-variable hypothesis builder for an operation in maps-to notation. (Contributed by NM, 27-Aug-2013.)

Assertion

Ref	Expression
nfmpo2	|- F/_ y ( x e. A , y e. B |-> C )

Proof of Theorem nfmpo2

Dummy variable z is distinct from all other variables.

Step	Hyp	Ref	Expression
1		df-mpo 5779	. 2 |- ( x e. A , y e. B |-> C ) = { <. <. x , y >. , z >. | ( ( x e. A /\ y e. B ) /\ z = C ) }
2		nfoprab2 5821	. 2 |- F/_ y { <. <. x , y >. , z >. | ( ( x e. A /\ y e. B ) /\ z = C ) }
3	1, 2	nfcxfr 2278	1 |- F/_ y ( x e. A , y e. B |-> C )

Syntax hints:   /\ wa 103   = wceq 1331   e. wcel 1480   F/_wnfc 2268   {coprab 5775   e. cmpo 5776

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-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121

This theorem depends on definitions:  df-bi 116  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-nfc 2270  df-oprab 5778  df-mpo 5779

This theorem is referenced by:  ovmpos  5894  ov2gf  5895  ovmpodxf  5896  ovmpodf  5902  ovmpodv2  5904  xpcomco  6720  mapxpen  6742  cnmpt21  12463  cnmpt2t  12465  cnmptcom  12470