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Theorem nfsbc1v 2898
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 2256 . 2  |-  F/_ x A
21nfsbc1 2897 1  |-  F/ x [. A  /  x ]. ph
Colors of variables: wff set class
Syntax hints:   F/wnf 1419   [.wsbc 2880
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 1406  ax-7 1407  ax-gen 1408  ax-ie1 1452  ax-ie2 1453  ax-8 1465  ax-11 1467  ax-4 1470  ax-17 1489  ax-i9 1493  ax-ial 1497  ax-i5r 1498  ax-ext 2097
This theorem depends on definitions:  df-bi 116  df-tru 1317  df-nf 1420  df-sb 1719  df-clab 2102  df-cleq 2108  df-clel 2111  df-nfc 2245  df-sbc 2881
This theorem is referenced by:  elrabsf  2917  cbvralcsf  3030  cbvrexcsf  3031  euotd  4144  findes  4485  omsinds  4503  elfvmptrab1  5481  ralrnmpt  5528  rexrnmpt  5529  dfopab2  6053  dfoprab3s  6054  mpoxopoveq  6103  findcard2  6749  findcard2s  6750  ac6sfi  6758  indpi  7114  nn0ind-raph  9122  uzind4s  9337  indstr  9340  fzrevral  9836  exfzdc  9968  uzsinds  10166  zsupcllemstep  11545  infssuzex  11549  prmind2  11708  bj-bdfindes  12981  bj-findes  13013
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