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Theorem nfsbc1v 2900
Description: Bound-variable hypothesis builder for class substitution. (Contributed by Mario Carneiro, 12-Oct-2016.)
Assertion
Ref Expression
nfsbc1v  |-  F/ x [. A  /  x ]. ph
Distinct variable group:    x, A
Allowed substitution hint:    ph( x)

Proof of Theorem nfsbc1v
StepHypRef Expression
1 nfcv 2258 . 2  |-  F/_ x A
21nfsbc1 2899 1  |-  F/ x [. A  /  x ]. ph
Colors of variables: wff set class
Syntax hints:   F/wnf 1421   [.wsbc 2882
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-5 1408  ax-7 1409  ax-gen 1410  ax-ie1 1454  ax-ie2 1455  ax-8 1467  ax-11 1469  ax-4 1472  ax-17 1491  ax-i9 1495  ax-ial 1499  ax-i5r 1500  ax-ext 2099
This theorem depends on definitions:  df-bi 116  df-tru 1319  df-nf 1422  df-sb 1721  df-clab 2104  df-cleq 2110  df-clel 2113  df-nfc 2247  df-sbc 2883
This theorem is referenced by:  elrabsf  2919  cbvralcsf  3032  cbvrexcsf  3033  euotd  4146  findes  4487  omsinds  4505  elfvmptrab1  5483  ralrnmpt  5530  rexrnmpt  5531  dfopab2  6055  dfoprab3s  6056  mpoxopoveq  6105  findcard2  6751  findcard2s  6752  ac6sfi  6760  indpi  7118  nn0ind-raph  9136  uzind4s  9353  indstr  9356  fzrevral  9853  exfzdc  9985  uzsinds  10183  zsupcllemstep  11565  infssuzex  11569  prmind2  11728  bj-bdfindes  13074  bj-findes  13106
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