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  4288  findes  4640  omsinds  4659  elfvmptrab1  5659  ralrnmpt  5707  rexrnmpt  5708  elovmporab  6127  elovmporab1w  6128  uchoice  6204  dfopab2  6256  dfoprab3s  6257  mpoxopoveq  6307  findcard2  6959  findcard2s  6960  ac6sfi  6968  opabfi  7008  dcfi  7056  indpi  7426  nn0ind-raph  9460  uzind4s  9681  indstr  9684  fzrevral  10197  exfzdc  10333  zsupcllemstep  10336  infssuzex  10340  uzsinds  10553  prmind2  12313  bj-bdfindes  15679  bj-findes  15711