Theorem nffvmpt1 5600

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 4145	. 2 |- F/_ x ( x e. A |-> B )
2		nfcv 2349	. 2 |- F/_ x C
3	1, 2	nffv 5599	1 |- F/_ x ( ( x e. A |-> B ) ` C )

Syntax hints:   F/_wnfc 2336   |-> cmpt 4113   ` cfv 5280

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 711  ax-5 1471  ax-7 1472  ax-gen 1473  ax-ie1 1517  ax-ie2 1518  ax-8 1528  ax-10 1529  ax-11 1530  ax-i12 1531  ax-bndl 1533  ax-4 1534  ax-17 1550  ax-i9 1554  ax-ial 1558  ax-i5r 1559  ax-ext 2188

This theorem depends on definitions:  df-bi 117  df-3an 983  df-tru 1376  df-nf 1485  df-sb 1787  df-clab 2193  df-cleq 2199  df-clel 2202  df-nfc 2338  df-rex 2491  df-v 2775  df-un 3174  df-sn 3644  df-pr 3645  df-op 3647  df-uni 3857  df-br 4052  df-opab 4114  df-mpt 4115  df-iota 5241  df-fv 5288

This theorem is referenced by:  fvmptt  5684  fmptco  5759  offval2  6187  ofrfval2  6188  mptelixpg  6834  dom2lem  6876  cc2  7399  fsumf1o  11776  fsum3cvg2  11780  fsumadd  11792  isummulc2  11812  isumshft  11876  fprodf1o  11974  prdsbas3  13194  txcnp  14818  cnmpt1t  14832  elplyd  15288