Theorem nfsbc1v 2969

Description: Bound-variable hypothesis builder for class substitution. (Contributed by Mario Carneiro, 12-Oct-2016.)

Assertion

Ref	Expression
nfsbc1v	⊢ Ⅎ𝑥[𝐴 / 𝑥]𝜑

Distinct variable group:   𝑥,𝐴

Allowed substitution hint:   𝜑(𝑥)

Proof of Theorem nfsbc1v

Step	Hyp	Ref	Expression
1		nfcv 2308	. 2 ⊢ Ⅎ𝑥𝐴
2	1	nfsbc1 2968	1 ⊢ Ⅎ𝑥[𝐴 / 𝑥]𝜑

Syntax hints:  Ⅎwnf 1448  [wsbc 2951

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 1435  ax-7 1436  ax-gen 1437  ax-ie1 1481  ax-ie2 1482  ax-8 1492  ax-11 1494  ax-4 1498  ax-17 1514  ax-i9 1518  ax-ial 1522  ax-i5r 1523  ax-ext 2147

This theorem depends on definitions:  df-bi 116  df-tru 1346  df-nf 1449  df-sb 1751  df-clab 2152  df-cleq 2158  df-clel 2161  df-nfc 2297  df-sbc 2952

This theorem is referenced by:  elrabsf  2989  cbvralcsf  3107  cbvrexcsf  3108  euotd  4232  findes  4580  omsinds  4599  elfvmptrab1  5580  ralrnmpt  5627  rexrnmpt  5628  dfopab2  6157  dfoprab3s  6158  mpoxopoveq  6208  findcard2  6855  findcard2s  6856  ac6sfi  6864  dcfi  6946  indpi  7283  nn0ind-raph  9308  uzind4s  9528  indstr  9531  fzrevral  10040  exfzdc  10175  uzsinds  10377  zsupcllemstep  11878  infssuzex  11882  prmind2  12052  bj-bdfindes  13831  bj-findes  13863