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Theorem nfsbc1v 2981
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 2319 . 2 𝑥𝐴
21nfsbc1 2980 1 𝑥[𝐴 / 𝑥]𝜑
Colors of variables: wff set class
Syntax hints:  wnf 1460  [wsbc 2962
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 1447  ax-7 1448  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-8 1504  ax-11 1506  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-tru 1356  df-nf 1461  df-sb 1763  df-clab 2164  df-cleq 2170  df-clel 2173  df-nfc 2308  df-sbc 2963
This theorem is referenced by:  elrabsf  3001  cbvralcsf  3119  cbvrexcsf  3120  euotd  4251  findes  4599  omsinds  4618  elfvmptrab1  5606  ralrnmpt  5654  rexrnmpt  5655  dfopab2  6184  dfoprab3s  6185  mpoxopoveq  6235  findcard2  6883  findcard2s  6884  ac6sfi  6892  dcfi  6974  indpi  7332  nn0ind-raph  9359  uzind4s  9579  indstr  9582  fzrevral  10091  exfzdc  10226  uzsinds  10428  zsupcllemstep  11929  infssuzex  11933  prmind2  12103  bj-bdfindes  14357  bj-findes  14389
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