Theorem nfmpt22 5592

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

Assertion

Ref	Expression
nfmpt22	|- F/_ y ( x e. A , y e. B |-> C )

Proof of Theorem nfmpt22

Dummy variable z is distinct from all other variables.

Step	Hyp	Ref	Expression
1		df-mpt2 5537	. 2 |- ( x e. A , y e. B |-> C ) = { <. <. x , y >. , z >. | ( ( x e. A /\ y e. B ) /\ z = C ) }
2		nfoprab2 5575	. 2 |- F/_ y { <. <. x , y >. , z >. | ( ( x e. A /\ y e. B ) /\ z = C ) }
3	1, 2	nfcxfr 2216	1 |- F/_ y ( x e. A , y e. B |-> C )

Syntax hints:   /\ wa 102   = wceq 1284   e. wcel 1433   F/_wnfc 2206   {coprab 5533   |-> cmpt2 5534

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 662  ax-5 1376  ax-7 1377  ax-gen 1378  ax-ie1 1422  ax-ie2 1423  ax-8 1435  ax-10 1436  ax-11 1437  ax-i12 1438  ax-bndl 1439  ax-4 1440  ax-17 1459  ax-i9 1463  ax-ial 1467  ax-i5r 1468  ax-ext 2063

This theorem depends on definitions:  df-bi 115  df-nf 1390  df-sb 1686  df-clab 2068  df-cleq 2074  df-clel 2077  df-nfc 2208  df-oprab 5536  df-mpt2 5537

This theorem is referenced by:  ovmpt2s  5644  ov2gf  5645  ovmpt2dxf  5646  ovmpt2df  5652  ovmpt2dv2  5654  xpcomco  6323