Theorem nfsbc1v 3070

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 2392	. 2 ⊢ Ⅎ𝑥𝐴
2	1	nfsbc1 3069	1 ⊢ Ⅎ𝑥[𝐴 / 𝑥]𝜑

This proof depends on syntax axioms:  Ⅎwnf 1513  [wsbc 3051

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1500  ax-7 1501  ax-gen 1502  ax-ie1 1546  ax-ie2 1547  ax-8 1557  ax-11 1559  ax-4 1563  ax-17 1579  ax-i9 1583  ax-ial 1587  ax-i5r 1588  ax-ext 2220

This proof depends on definitions:  df-bi 117  df-tru 1405  df-nf 1514  df-sb 1816  df-clab 2225  df-cleq 2231  df-clel 2234  df-nfc 2381  df-sbc 3052

This theorem is used by:  elrabsf  3090  cbvralcsf  3210  cbvrexcsf  3211  rabsnifsb  3777  euotd  4397  findes  4752  omsinds  4771  elfvmptrab1  5804  ralrnmpt  5853  rexrnmpt  5854  elovmporab  6292  elovmporab1w  6293  uchoice  6375  dfopab2  6427  dfoprab3s  6428  mpoxopoveq  6515  findcard2  7197  findcard2s  7198  ac6sfi  7206  opabfi  7251  dcfi  7320  indpi  7715  nn0ind-raph  9774  uzind4s  10006  indstr  10009  fzrevral  10529  exfzdc  10676  zsupcllemstep  10679  infssuzex  10683  uzsinds  10902  prmind2  12923  gropd  16493  grstructd2dom  16494  bj-bdfindes  17180  bj-findes  17212