Theorem nfsbc1v 2922

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 2279	. 2 ⊢ Ⅎ𝑥𝐴
2	1	nfsbc1 2921	1 ⊢ Ⅎ𝑥[𝐴 / 𝑥]𝜑

Syntax hints:  Ⅎwnf 1436  [wsbc 2904

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 2119

This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2124  df-cleq 2130  df-clel 2133  df-nfc 2268  df-sbc 2905

This theorem is referenced by:  elrabsf  2942  cbvralcsf  3057  cbvrexcsf  3058  euotd  4171  findes  4512  omsinds  4530  elfvmptrab1  5508  ralrnmpt  5555  rexrnmpt  5556  dfopab2  6080  dfoprab3s  6081  mpoxopoveq  6130  findcard2  6776  findcard2s  6777  ac6sfi  6785  indpi  7143  nn0ind-raph  9161  uzind4s  9378  indstr  9381  fzrevral  9878  exfzdc  10010  uzsinds  10208  zsupcllemstep  11627  infssuzex  11631  prmind2  11790  bj-bdfindes  13136  bj-findes  13168