Theorem nfmpo2 5890

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 5830	. 2 |- ( x e. A , y e. B |-> C ) = { <. <. x , y >. , z >. | ( ( x e. A /\ y e. B ) /\ z = C ) }
2		nfoprab2 5872	. 2 |- F/_ y { <. <. x , y >. , z >. | ( ( x e. A /\ y e. B ) /\ z = C ) }
3	1, 2	nfcxfr 2296	1 |- F/_ y ( x e. A , y e. B |-> C )

Syntax hints:   /\ wa 103   = wceq 1335   e. wcel 2128   F/_wnfc 2286   {coprab 5826   e. cmpo 5827

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-ext 2139

This theorem depends on definitions:  df-bi 116  df-nf 1441  df-sb 1743  df-clab 2144  df-cleq 2150  df-clel 2153  df-nfc 2288  df-oprab 5829  df-mpo 5830

This theorem is referenced by:  ovmpos  5945  ov2gf  5946  ovmpodxf  5947  ovmpodf  5953  ovmpodv2  5955  xpcomco  6772  mapxpen  6794  cnmpt21  12733  cnmpt2t  12735  cnmptcom  12740