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Theorem nfsbc1v 2782
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 2178 . 2 𝑥𝐴
21nfsbc1 2781 1 𝑥[𝐴 / 𝑥]𝜑
Colors of variables: wff set class
Syntax hints:  wnf 1349  [wsbc 2764
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 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-11 1397  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022
This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-sbc 2765
This theorem is referenced by:  elrabsf  2801  cbvralcsf  2908  cbvrexcsf  2909  euotd  3991  findes  4326  ralrnmpt  5309  rexrnmpt  5310  dfopab2  5815  dfoprab3s  5816  mpt2xopoveq  5855  findcard2  6346  findcard2s  6347  ac6sfi  6352  indpi  6438  nn0ind-raph  8353  uzind4s  8531  indstr  8534  fzrevral  8965  bj-bdfindes  10048  bj-findes  10080
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