Theorem nfsbc1v 3004

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 2336	. 2 ⊢ Ⅎ𝑥𝐴
2	1	nfsbc1 3003	1 ⊢ Ⅎ𝑥[𝐴 / 𝑥]𝜑

Syntax hints:  Ⅎwnf 1471  [wsbc 2985

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 1458  ax-7 1459  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-11 1517  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-i5r 1546  ax-ext 2175

This theorem depends on definitions:  df-bi 117  df-tru 1367  df-nf 1472  df-sb 1774  df-clab 2180  df-cleq 2186  df-clel 2189  df-nfc 2325  df-sbc 2986

This theorem is referenced by:  elrabsf  3024  cbvralcsf  3143  cbvrexcsf  3144  euotd  4283  findes  4635  omsinds  4654  elfvmptrab1  5652  ralrnmpt  5700  rexrnmpt  5701  elovmporab  6118  elovmporab1w  6119  uchoice  6190  dfopab2  6242  dfoprab3s  6243  mpoxopoveq  6293  findcard2  6945  findcard2s  6946  ac6sfi  6954  opabfi  6992  dcfi  7040  indpi  7402  nn0ind-raph  9434  uzind4s  9655  indstr  9658  fzrevral  10171  exfzdc  10307  uzsinds  10515  zsupcllemstep  12082  infssuzex  12086  prmind2  12258  bj-bdfindes  15441  bj-findes  15473