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Theorem nfsbc1v 2993
Description: Bound-variable hypothesis builder for class substitution. (Contributed by Mario Carneiro, 12-Oct-2016.)
Assertion
Ref Expression
nfsbc1v 𝑥[𝐴 / 𝑥]𝜑
Distinct variable group:   𝑥,𝐴
Allowed substitution hint:   𝜑(𝑥)

Proof of Theorem nfsbc1v
StepHypRef Expression
1 nfcv 2329 . 2 𝑥𝐴
21nfsbc1 2992 1 𝑥[𝐴 / 𝑥]𝜑
Colors of variables: wff set class
Syntax hints:  wnf 1470  [wsbc 2974
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-5 1457  ax-7 1458  ax-gen 1459  ax-ie1 1503  ax-ie2 1504  ax-8 1514  ax-11 1516  ax-4 1520  ax-17 1536  ax-i9 1540  ax-ial 1544  ax-i5r 1545  ax-ext 2169
This theorem depends on definitions:  df-bi 117  df-tru 1366  df-nf 1471  df-sb 1773  df-clab 2174  df-cleq 2180  df-clel 2183  df-nfc 2318  df-sbc 2975
This theorem is referenced by:  elrabsf  3013  cbvralcsf  3131  cbvrexcsf  3132  euotd  4266  findes  4614  omsinds  4633  elfvmptrab1  5623  ralrnmpt  5671  rexrnmpt  5672  dfopab2  6203  dfoprab3s  6204  mpoxopoveq  6254  findcard2  6902  findcard2s  6903  ac6sfi  6911  dcfi  6993  indpi  7354  nn0ind-raph  9383  uzind4s  9603  indstr  9606  fzrevral  10118  exfzdc  10253  uzsinds  10455  zsupcllemstep  11959  infssuzex  11963  prmind2  12133  bj-bdfindes  14972  bj-findes  15004
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