Theorem nfmpo2 6012

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 5948	. 2 |- ( x e. A , y e. B |-> C ) = { <. <. x , y >. , z >. | ( ( x e. A /\ y e. B ) /\ z = C ) }
2		nfoprab2 5994	. 2 |- F/_ y { <. <. x , y >. , z >. | ( ( x e. A /\ y e. B ) /\ z = C ) }
3	1, 2	nfcxfr 2344	1 |- F/_ y ( x e. A , y e. B |-> C )

Syntax hints:   /\ wa 104   = wceq 1372   e. wcel 2175   F/_wnfc 2334   {coprab 5944   e. cmpo 5945

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 710  ax-5 1469  ax-7 1470  ax-gen 1471  ax-ie1 1515  ax-ie2 1516  ax-8 1526  ax-10 1527  ax-11 1528  ax-i12 1529  ax-bndl 1531  ax-4 1532  ax-17 1548  ax-i9 1552  ax-ial 1556  ax-i5r 1557  ax-ext 2186

This theorem depends on definitions:  df-bi 117  df-nf 1483  df-sb 1785  df-clab 2191  df-cleq 2197  df-clel 2200  df-nfc 2336  df-oprab 5947  df-mpo 5948

This theorem is referenced by:  ovmpos  6068  ov2gf  6069  ovmpodxf  6070  ovmpodf  6076  ovmpodv2  6078  xpcomco  6920  mapxpen  6944  cnmpt21  14705  cnmpt2t  14707  cnmptcom  14712