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Theorem nffvmpt1 5528
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 4098 . 2 𝑥(𝑥𝐴𝐵)
2 nfcv 2319 . 2 𝑥𝐶
31, 2nffv 5527 1 𝑥((𝑥𝐴𝐵)‘𝐶)
Colors of variables: wff set class
Syntax hints:  wnfc 2306  cmpt 4066  cfv 5218
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 709  ax-5 1447  ax-7 1448  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-8 1504  ax-10 1505  ax-11 1506  ax-i12 1507  ax-bndl 1509  ax-4 1510  ax-17 1526  ax-i9 1530  ax-ial 1534  ax-i5r 1535  ax-ext 2159
This theorem depends on definitions:  df-bi 117  df-3an 980  df-tru 1356  df-nf 1461  df-sb 1763  df-clab 2164  df-cleq 2170  df-clel 2173  df-nfc 2308  df-rex 2461  df-v 2741  df-un 3135  df-sn 3600  df-pr 3601  df-op 3603  df-uni 3812  df-br 4006  df-opab 4067  df-mpt 4068  df-iota 5180  df-fv 5226
This theorem is referenced by:  fvmptt  5609  fmptco  5684  offval2  6100  ofrfval2  6101  mptelixpg  6736  dom2lem  6774  cc2  7268  fsumf1o  11400  fsum3cvg2  11404  fsumadd  11416  isummulc2  11436  isumshft  11500  fprodf1o  11598  txcnp  13810  cnmpt1t  13824
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