Theorem nfsbc1v 3047

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 2372	. 2 ⊢ Ⅎ𝑥𝐴
2	1	nfsbc1 3046	1 ⊢ Ⅎ𝑥[𝐴 / 𝑥]𝜑

Syntax hints:  Ⅎwnf 1506  [wsbc 3028

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 1493  ax-7 1494  ax-gen 1495  ax-ie1 1539  ax-ie2 1540  ax-8 1550  ax-11 1552  ax-4 1556  ax-17 1572  ax-i9 1576  ax-ial 1580  ax-i5r 1581  ax-ext 2211

This theorem depends on definitions:  df-bi 117  df-tru 1398  df-nf 1507  df-sb 1809  df-clab 2216  df-cleq 2222  df-clel 2225  df-nfc 2361  df-sbc 3029

This theorem is referenced by:  elrabsf  3067  cbvralcsf  3187  cbvrexcsf  3188  euotd  4340  findes  4694  omsinds  4713  elfvmptrab1  5728  ralrnmpt  5776  rexrnmpt  5777  elovmporab  6204  elovmporab1w  6205  uchoice  6281  dfopab2  6333  dfoprab3s  6334  mpoxopoveq  6384  findcard2  7047  findcard2s  7048  ac6sfi  7056  opabfi  7096  dcfi  7144  indpi  7525  nn0ind-raph  9560  uzind4s  9781  indstr  9784  fzrevral  10297  exfzdc  10441  zsupcllemstep  10444  infssuzex  10448  uzsinds  10661  prmind2  12637  gropd  15842  grstructd2dom  15843  bj-bdfindes  16270  bj-findes  16302