Theorem nfsbc1v 3064

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 2386	. 2 ⊢ Ⅎ𝑥𝐴
2	1	nfsbc1 3063	1 ⊢ Ⅎ𝑥[𝐴 / 𝑥]𝜑

Syntax hints:  Ⅎwnf 1509  [wsbc 3045

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 1496  ax-7 1497  ax-gen 1498  ax-ie1 1542  ax-ie2 1543  ax-8 1553  ax-11 1555  ax-4 1559  ax-17 1575  ax-i9 1579  ax-ial 1583  ax-i5r 1584  ax-ext 2216

This theorem depends on definitions:  df-bi 117  df-tru 1401  df-nf 1510  df-sb 1812  df-clab 2221  df-cleq 2227  df-clel 2230  df-nfc 2375  df-sbc 3046

This theorem is referenced by:  elrabsf  3084  cbvralcsf  3204  cbvrexcsf  3205  rabsnifsb  3762  euotd  4376  findes  4730  omsinds  4749  elfvmptrab1  5777  ralrnmpt  5824  rexrnmpt  5825  elovmporab  6262  elovmporab1w  6263  uchoice  6344  dfopab2  6396  dfoprab3s  6397  mpoxopoveq  6484  findcard2  7159  findcard2s  7160  ac6sfi  7168  opabfi  7213  dcfi  7281  indpi  7673  nn0ind-raph  9713  uzind4s  9940  indstr  9943  fzrevral  10461  exfzdc  10608  zsupcllemstep  10611  infssuzex  10615  uzsinds  10830  prmind2  12842  gropd  16168  grstructd2dom  16169  bj-bdfindes  16845  bj-findes  16877