Theorem nfsbc1v 3008

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 2339	. 2 ⊢ Ⅎ𝑥𝐴
2	1	nfsbc1 3007	1 ⊢ Ⅎ𝑥[𝐴 / 𝑥]𝜑

Syntax hints:  Ⅎwnf 1474  [wsbc 2989

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 1461  ax-7 1462  ax-gen 1463  ax-ie1 1507  ax-ie2 1508  ax-8 1518  ax-11 1520  ax-4 1524  ax-17 1540  ax-i9 1544  ax-ial 1548  ax-i5r 1549  ax-ext 2178

This theorem depends on definitions:  df-bi 117  df-tru 1367  df-nf 1475  df-sb 1777  df-clab 2183  df-cleq 2189  df-clel 2192  df-nfc 2328  df-sbc 2990

This theorem is referenced by:  elrabsf  3028  cbvralcsf  3147  cbvrexcsf  3148  euotd  4287  findes  4639  omsinds  4658  elfvmptrab1  5656  ralrnmpt  5704  rexrnmpt  5705  elovmporab  6123  elovmporab1w  6124  uchoice  6195  dfopab2  6247  dfoprab3s  6248  mpoxopoveq  6298  findcard2  6950  findcard2s  6951  ac6sfi  6959  opabfi  6999  dcfi  7047  indpi  7409  nn0ind-raph  9443  uzind4s  9664  indstr  9667  fzrevral  10180  exfzdc  10316  zsupcllemstep  10319  infssuzex  10323  uzsinds  10536  prmind2  12288  bj-bdfindes  15595  bj-findes  15627