Theorem nfmpo2 6071

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 6005	. 2 |- ( x e. A , y e. B |-> C ) = { <. <. x , y >. , z >. | ( ( x e. A /\ y e. B ) /\ z = C ) }
2		nfoprab2 6053	. 2 |- F/_ y { <. <. x , y >. , z >. | ( ( x e. A /\ y e. B ) /\ z = C ) }
3	1, 2	nfcxfr 2369	1 |- F/_ y ( x e. A , y e. B |-> C )

Syntax hints:   /\ wa 104   = wceq 1395   e. wcel 2200   F/_wnfc 2359   {coprab 6001   e. cmpo 6002

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 714  ax-5 1493  ax-7 1494  ax-gen 1495  ax-ie1 1539  ax-ie2 1540  ax-8 1550  ax-10 1551  ax-11 1552  ax-i12 1553  ax-bndl 1555  ax-4 1556  ax-17 1572  ax-i9 1576  ax-ial 1580  ax-i5r 1581  ax-ext 2211

This theorem depends on definitions:  df-bi 117  df-nf 1507  df-sb 1809  df-clab 2216  df-cleq 2222  df-clel 2225  df-nfc 2361  df-oprab 6004  df-mpo 6005

This theorem is referenced by:  ovmpos  6127  ov2gf  6128  ovmpodxf  6129  ovmpodf  6135  ovmpodv2  6137  xpcomco  6981  mapxpen  7005  cnmpt21  14959  cnmpt2t  14961  cnmptcom  14966