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Theorem nfsbc1v 2805
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 2194 . 2  |-  F/_ x A
21nfsbc1 2804 1  |-  F/ x [. A  /  x ]. ph
Colors of variables: wff set class
Syntax hints:   F/wnf 1365   [.wsbc 2787
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-11 1413  ax-4 1416  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-i5r 1444  ax-ext 2038
This theorem depends on definitions:  df-bi 114  df-tru 1262  df-nf 1366  df-sb 1662  df-clab 2043  df-cleq 2049  df-clel 2052  df-nfc 2183  df-sbc 2788
This theorem is referenced by:  elrabsf  2824  cbvralcsf  2936  cbvrexcsf  2937  euotd  4019  findes  4354  ralrnmpt  5337  rexrnmpt  5338  dfopab2  5843  dfoprab3s  5844  mpt2xopoveq  5886  findcard2  6377  findcard2s  6378  ac6sfi  6383  indpi  6498  nn0ind-raph  8414  uzind4s  8629  indstr  8632  fzrevral  9069  bj-bdfindes  10461  bj-findes  10493
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