Theorem nfmpo2 6099

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 6033	. 2 |- ( x e. A , y e. B |-> C ) = { <. <. x , y >. , z >. | ( ( x e. A /\ y e. B ) /\ z = C ) }
2		nfoprab2 6081	. 2 |- F/_ y { <. <. x , y >. , z >. | ( ( x e. A /\ y e. B ) /\ z = C ) }
3	1, 2	nfcxfr 2372	1 |- F/_ y ( x e. A , y e. B |-> C )

Syntax hints:   /\ wa 104   = wceq 1398   e. wcel 2202   F/_wnfc 2362   {coprab 6029   e. cmpo 6030

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 717  ax-5 1496  ax-7 1497  ax-gen 1498  ax-ie1 1542  ax-ie2 1543  ax-8 1553  ax-10 1554  ax-11 1555  ax-i12 1556  ax-bndl 1558  ax-4 1559  ax-17 1575  ax-i9 1579  ax-ial 1583  ax-i5r 1584  ax-ext 2213

This theorem depends on definitions:  df-bi 117  df-nf 1510  df-sb 1811  df-clab 2218  df-cleq 2224  df-clel 2227  df-nfc 2364  df-oprab 6032  df-mpo 6033

This theorem is referenced by:  ovmpos  6155  ov2gf  6156  ovmpodxf  6157  ovmpodf  6163  ovmpodv2  6165  xpcomco  7053  mapxpen  7077  cnmpt21  15085  cnmpt2t  15087  cnmptcom  15092