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Theorem nffvmpt1 5186
 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 3850 . 2 𝑥(𝑥𝐴𝐵)
2 nfcv 2178 . 2 𝑥𝐶
31, 2nffv 5185 1 𝑥((𝑥𝐴𝐵)‘𝐶)
 Colors of variables: wff set class Syntax hints:  Ⅎwnfc 2165   ↦ cmpt 3818  ‘cfv 4902 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-3an 887  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-rex 2312  df-v 2559  df-un 2922  df-sn 3381  df-pr 3382  df-op 3384  df-uni 3581  df-br 3765  df-opab 3819  df-mpt 3820  df-iota 4867  df-fv 4910 This theorem is referenced by:  fvmptt  5262  fmptco  5330  offval2  5726  ofrfval2  5727  dom2lem  6252
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