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Theorem nfsbc1v 2776
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 2175 . 2 xA
21nfsbc1 2775 1 x[A / x]φ
Colors of variables: wff set class
Syntax hints:  wnf 1346  [wsbc 2758
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-11 1394  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-sbc 2759
This theorem is referenced by:  elrabsf  2795  cbvralcsf  2902  cbvrexcsf  2903  euotd  3982  findes  4269  ralrnmpt  5252  rexrnmpt  5253  dfopab2  5757  dfoprab3s  5758  mpt2xopoveq  5796  indpi  6326  nn0ind-raph  8111  uzind4s  8289  indstr  8292  fzrevral  8717  bj-bdfindes  9383  bj-findes  9411
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