Theorem nffvmpt1 5310

Description: Bound-variable hypothesis builder for mapping, special case. (Contributed by Mario Carneiro, 25-Dec-2016.)

Assertion

Ref	Expression
nffvmpt1	|- F/_ x ( ( x e. A |-> B ) ` C )

Distinct variable group:   x, C

Allowed substitution hints:   A( x)   B( x)

Proof of Theorem nffvmpt1

Step	Hyp	Ref	Expression
1		nfmpt1 3929	. 2 |- F/_ x ( x e. A |-> B )
2		nfcv 2228	. 2 |- F/_ x C
3	1, 2	nffv 5309	1 |- F/_ x ( ( x e. A |-> B ) ` C )

Syntax hints:   F/_wnfc 2215   |-> cmpt 3897   ` cfv 5010

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 665  ax-5 1381  ax-7 1382  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-8 1440  ax-10 1441  ax-11 1442  ax-i12 1443  ax-bndl 1444  ax-4 1445  ax-17 1464  ax-i9 1468  ax-ial 1472  ax-i5r 1473  ax-ext 2070

This theorem depends on definitions:  df-bi 115  df-3an 926  df-tru 1292  df-nf 1395  df-sb 1693  df-clab 2075  df-cleq 2081  df-clel 2084  df-nfc 2217  df-rex 2365  df-v 2621  df-un 3003  df-sn 3450  df-pr 3451  df-op 3453  df-uni 3652  df-br 3844  df-opab 3898  df-mpt 3899  df-iota 4975  df-fv 5018

This theorem is referenced by:  fvmptt  5388  fmptco  5458  offval2  5862  ofrfval2  5863  dom2lem  6479  fsumf1o  10769  fisumcvg2  10773  fsum3cvg2  10774  fsumadd  10787  isummulc2  10807  isumshft  10871