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Theorem nffvmpt1 5479
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 4057 . 2 𝑥(𝑥𝐴𝐵)
2 nfcv 2299 . 2 𝑥𝐶
31, 2nffv 5478 1 𝑥((𝑥𝐴𝐵)‘𝐶)
Colors of variables: wff set class
Syntax hints:  wnfc 2286  cmpt 4025  cfv 5170
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 699  ax-5 1427  ax-7 1428  ax-gen 1429  ax-ie1 1473  ax-ie2 1474  ax-8 1484  ax-10 1485  ax-11 1486  ax-i12 1487  ax-bndl 1489  ax-4 1490  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2139
This theorem depends on definitions:  df-bi 116  df-3an 965  df-tru 1338  df-nf 1441  df-sb 1743  df-clab 2144  df-cleq 2150  df-clel 2153  df-nfc 2288  df-rex 2441  df-v 2714  df-un 3106  df-sn 3566  df-pr 3567  df-op 3569  df-uni 3773  df-br 3966  df-opab 4026  df-mpt 4027  df-iota 5135  df-fv 5178
This theorem is referenced by:  fvmptt  5559  fmptco  5633  offval2  6047  ofrfval2  6048  mptelixpg  6679  dom2lem  6717  cc2  7187  fsumf1o  11287  fsum3cvg2  11291  fsumadd  11303  isummulc2  11323  isumshft  11387  fprodf1o  11485  txcnp  12671  cnmpt1t  12685
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