Theorem nfmpt1 4096

Description: Bound-variable hypothesis builder for the maps-to notation. (Contributed by FL, 17-Feb-2008.)

Assertion

Ref	Expression
nfmpt1	|- F/_ x ( x e. A |-> B )

Proof of Theorem nfmpt1

Dummy variable z is distinct from all other variables.

Step	Hyp	Ref	Expression
1		df-mpt 4066	. 2 |- ( x e. A |-> B ) = { <. x , z >. | ( x e. A /\ z = B ) }
2		nfopab1 4072	. 2 |- F/_ x { <. x , z >. | ( x e. A /\ z = B ) }
3	1, 2	nfcxfr 2316	1 |- F/_ x ( x e. A |-> B )

Syntax hints:   /\ wa 104   = wceq 1353   e. wcel 2148   F/_wnfc 2306   {copab 4063   |-> cmpt 4064

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 709  ax-5 1447  ax-7 1448  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-8 1504  ax-10 1505  ax-11 1506  ax-i12 1507  ax-bndl 1509  ax-4 1510  ax-17 1526  ax-i9 1530  ax-ial 1534  ax-i5r 1535  ax-ext 2159

This theorem depends on definitions:  df-bi 117  df-nf 1461  df-sb 1763  df-clab 2164  df-cleq 2170  df-clel 2173  df-nfc 2308  df-opab 4065  df-mpt 4066

This theorem is referenced by:  nffvmpt1  5526  fvmptss2  5591  fvmptssdm  5600  fvmptdf  5603  mpteqb  5606  fvmptf  5608  ralrnmpt  5658  rexrnmpt  5659  f1ompt  5667  f1mpt  5771  fliftfun  5796  dom2lem  6771  mapxpen  6847  mkvprop  7155  cc3  7266  nfcprod1  11561  cnmpt11  13753  lgseisenlem2  14421