Theorem nfsbc1v 3024

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 2350	. 2 ⊢ Ⅎ𝑥𝐴
2	1	nfsbc1 3023	1 ⊢ Ⅎ𝑥[𝐴 / 𝑥]𝜑

Syntax hints:  Ⅎwnf 1484  [wsbc 3005

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 1471  ax-7 1472  ax-gen 1473  ax-ie1 1517  ax-ie2 1518  ax-8 1528  ax-11 1530  ax-4 1534  ax-17 1550  ax-i9 1554  ax-ial 1558  ax-i5r 1559  ax-ext 2189

This theorem depends on definitions:  df-bi 117  df-tru 1376  df-nf 1485  df-sb 1787  df-clab 2194  df-cleq 2200  df-clel 2203  df-nfc 2339  df-sbc 3006

This theorem is referenced by:  elrabsf  3044  cbvralcsf  3164  cbvrexcsf  3165  euotd  4317  findes  4669  omsinds  4688  elfvmptrab1  5697  ralrnmpt  5745  rexrnmpt  5746  elovmporab  6169  elovmporab1w  6170  uchoice  6246  dfopab2  6298  dfoprab3s  6299  mpoxopoveq  6349  findcard2  7012  findcard2s  7013  ac6sfi  7021  opabfi  7061  dcfi  7109  indpi  7490  nn0ind-raph  9525  uzind4s  9746  indstr  9749  fzrevral  10262  exfzdc  10406  zsupcllemstep  10409  infssuzex  10413  uzsinds  10626  prmind2  12557  gropd  15761  grstructd2dom  15762  bj-bdfindes  16084  bj-findes  16116