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  5731  ralrnmpt  5779  rexrnmpt  5780  elovmporab  6211  elovmporab1w  6212  uchoice  6289  dfopab2  6341  dfoprab3s  6342  mpoxopoveq  6392  findcard2  7059  findcard2s  7060  ac6sfi  7068  opabfi  7111  dcfi  7159  indpi  7540  nn0ind-raph  9575  uzind4s  9797  indstr  9800  fzrevral  10313  exfzdc  10458  zsupcllemstep  10461  infssuzex  10465  uzsinds  10678  prmind2  12657  gropd  15863  grstructd2dom  15864  bj-bdfindes  16367  bj-findes  16399