Theorem nfsbc1v 2927

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 2281	. 2 ⊢ Ⅎ𝑥𝐴
2	1	nfsbc1 2926	1 ⊢ Ⅎ𝑥[𝐴 / 𝑥]𝜑

Syntax hints:  Ⅎwnf 1436  [wsbc 2909

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-11 1484  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121

This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-nfc 2270  df-sbc 2910

This theorem is referenced by:  elrabsf  2947  cbvralcsf  3062  cbvrexcsf  3063  euotd  4176  findes  4517  omsinds  4535  elfvmptrab1  5515  ralrnmpt  5562  rexrnmpt  5563  dfopab2  6087  dfoprab3s  6088  mpoxopoveq  6137  findcard2  6783  findcard2s  6784  ac6sfi  6792  indpi  7150  nn0ind-raph  9168  uzind4s  9385  indstr  9388  fzrevral  9885  exfzdc  10017  uzsinds  10215  zsupcllemstep  11638  infssuzex  11642  prmind2  11801  bj-bdfindes  13147  bj-findes  13179