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  4341  findes  4695  omsinds  4714  elfvmptrab1  5729  ralrnmpt  5777  rexrnmpt  5778  elovmporab  6205  elovmporab1w  6206  uchoice  6283  dfopab2  6335  dfoprab3s  6336  mpoxopoveq  6386  findcard2  7051  findcard2s  7052  ac6sfi  7060  opabfi  7100  dcfi  7148  indpi  7529  nn0ind-raph  9564  uzind4s  9785  indstr  9788  fzrevral  10301  exfzdc  10446  zsupcllemstep  10449  infssuzex  10453  uzsinds  10666  prmind2  12642  gropd  15848  grstructd2dom  15849  bj-bdfindes  16312  bj-findes  16344