Theorem nfsbc1v 2981

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 2319	. 2 ⊢ Ⅎ𝑥𝐴
2	1	nfsbc1 2980	1 ⊢ Ⅎ𝑥[𝐴 / 𝑥]𝜑

Syntax hints:  Ⅎwnf 1460  [wsbc 2962

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1447  ax-7 1448  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-8 1504  ax-11 1506  ax-4 1510  ax-17 1526  ax-i9 1530  ax-ial 1534  ax-i5r 1535  ax-ext 2159

This theorem depends on definitions:  df-bi 117  df-tru 1356  df-nf 1461  df-sb 1763  df-clab 2164  df-cleq 2170  df-clel 2173  df-nfc 2308  df-sbc 2963

This theorem is referenced by:  elrabsf  3001  cbvralcsf  3119  cbvrexcsf  3120  euotd  4252  findes  4600  omsinds  4619  elfvmptrab1  5607  ralrnmpt  5655  rexrnmpt  5656  dfopab2  6185  dfoprab3s  6186  mpoxopoveq  6236  findcard2  6884  findcard2s  6885  ac6sfi  6893  dcfi  6975  indpi  7336  nn0ind-raph  9364  uzind4s  9584  indstr  9587  fzrevral  10098  exfzdc  10233  uzsinds  10435  zsupcllemstep  11936  infssuzex  11940  prmind2  12110  bj-bdfindes  14472  bj-findes  14504