Theorem nfmpt1 4226

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 4195	. 2 |- ( x e. A |-> B ) = { <. x , z >. | ( x e. A /\ z = B ) }
2		nfopab1 4201	. 2 |- F/_ x { <. x , z >. | ( x e. A /\ z = B ) }
3	1, 2	nfcxfr 2389	1 |- F/_ x ( x e. A |-> B )

This proof depends on syntax axioms:   /\ wa 104   = wceq 1402   e. wcel 2209   F/_wnfc 2379   {copab 4192   |-> cmpt 4193

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 721  ax-5 1500  ax-7 1501  ax-gen 1502  ax-ie1 1546  ax-ie2 1547  ax-8 1557  ax-10 1558  ax-11 1559  ax-i12 1560  ax-bndl 1562  ax-4 1563  ax-17 1579  ax-i9 1583  ax-ial 1587  ax-i5r 1588  ax-ext 2220

This proof depends on definitions:  df-bi 117  df-nf 1514  df-sb 1816  df-clab 2225  df-cleq 2231  df-clel 2234  df-nfc 2381  df-opab 4194  df-mpt 4195

This theorem is used by:  nffvmpt1  5709  fvmptss2  5783  fvmptssdm  5793  fvmptdf  5796  mpteqb  5799  fvmptf  5801  ralrnmpt  5853  rexrnmpt  5854  f1ompt  5862  f1mpt  5980  fliftfun  6005  dom2lem  7062  mapxpen  7152  mkvprop  7504  cc3  7640  nfcprod1  12346  ballotfilem7  13337  cnmpt11  15509  lgseisenlem2  16395