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Theorem nffvmpt1 5425
 Description: Bound-variable hypothesis builder for mapping, special case. (Contributed by Mario Carneiro, 25-Dec-2016.)
Assertion
Ref Expression
nffvmpt1 𝑥((𝑥𝐴𝐵)‘𝐶)
Distinct variable group:   𝑥,𝐶
Allowed substitution hints:   𝐴(𝑥)   𝐵(𝑥)

Proof of Theorem nffvmpt1
StepHypRef Expression
1 nfmpt1 4016 . 2 𝑥(𝑥𝐴𝐵)
2 nfcv 2279 . 2 𝑥𝐶
31, 2nffv 5424 1 𝑥((𝑥𝐴𝐵)‘𝐶)
 Colors of variables: wff set class Syntax hints:  Ⅎwnfc 2266   ↦ cmpt 3984  ‘cfv 5118 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2119 This theorem depends on definitions:  df-bi 116  df-3an 964  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2124  df-cleq 2130  df-clel 2133  df-nfc 2268  df-rex 2420  df-v 2683  df-un 3070  df-sn 3528  df-pr 3529  df-op 3531  df-uni 3732  df-br 3925  df-opab 3985  df-mpt 3986  df-iota 5083  df-fv 5126 This theorem is referenced by:  fvmptt  5505  fmptco  5579  offval2  5990  ofrfval2  5991  mptelixpg  6621  dom2lem  6659  fsumf1o  11152  fsum3cvg2  11156  fsumadd  11168  isummulc2  11188  isumshft  11252  txcnp  12429  cnmpt1t  12443
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