Theorem nfsbc1v 3070

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 2392	. 2 ⊢ Ⅎ𝑥𝐴
2	1	nfsbc1 3069	1 ⊢ Ⅎ𝑥[𝐴 / 𝑥]𝜑

Syntax hints:  Ⅎwnf 1513  [wsbc 3051

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 1500  ax-7 1501  ax-gen 1502  ax-ie1 1546  ax-ie2 1547  ax-8 1557  ax-11 1559  ax-4 1563  ax-17 1579  ax-i9 1583  ax-ial 1587  ax-i5r 1588  ax-ext 2220

This theorem depends on definitions:  df-bi 117  df-tru 1405  df-nf 1514  df-sb 1816  df-clab 2225  df-cleq 2231  df-clel 2234  df-nfc 2381  df-sbc 3052

This theorem is referenced by:  elrabsf  3090  cbvralcsf  3210  cbvrexcsf  3211  rabsnifsb  3773  euotd  4390  findes  4745  omsinds  4764  elfvmptrab1  5794  ralrnmpt  5841  rexrnmpt  5842  elovmporab  6279  elovmporab1w  6280  uchoice  6361  dfopab2  6413  dfoprab3s  6414  mpoxopoveq  6501  findcard2  7183  findcard2s  7184  ac6sfi  7192  opabfi  7237  dcfi  7305  indpi  7699  nn0ind-raph  9742  uzind4s  9969  indstr  9972  fzrevral  10490  exfzdc  10637  zsupcllemstep  10640  infssuzex  10644  uzsinds  10859  prmind2  12876  gropd  16202  grstructd2dom  16203  bj-bdfindes  16889  bj-findes  16921