Theorem nfsbc1v 3017

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 2348	. 2 ⊢ Ⅎ𝑥𝐴
2	1	nfsbc1 3016	1 ⊢ Ⅎ𝑥[𝐴 / 𝑥]𝜑

Syntax hints:  Ⅎwnf 1483  [wsbc 2998

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 1470  ax-7 1471  ax-gen 1472  ax-ie1 1516  ax-ie2 1517  ax-8 1527  ax-11 1529  ax-4 1533  ax-17 1549  ax-i9 1553  ax-ial 1557  ax-i5r 1558  ax-ext 2187

This theorem depends on definitions:  df-bi 117  df-tru 1376  df-nf 1484  df-sb 1786  df-clab 2192  df-cleq 2198  df-clel 2201  df-nfc 2337  df-sbc 2999

This theorem is referenced by:  elrabsf  3037  cbvralcsf  3156  cbvrexcsf  3157  euotd  4299  findes  4651  omsinds  4670  elfvmptrab1  5674  ralrnmpt  5722  rexrnmpt  5723  elovmporab  6146  elovmporab1w  6147  uchoice  6223  dfopab2  6275  dfoprab3s  6276  mpoxopoveq  6326  findcard2  6986  findcard2s  6987  ac6sfi  6995  opabfi  7035  dcfi  7083  indpi  7455  nn0ind-raph  9490  uzind4s  9711  indstr  9714  fzrevral  10227  exfzdc  10369  zsupcllemstep  10372  infssuzex  10376  uzsinds  10589  prmind2  12442  gropd  15644  grstructd2dom  15645  bj-bdfindes  15885  bj-findes  15917