Theorem nfsbc1v 2951

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 2296	. 2 ⊢ Ⅎ𝑥𝐴
2	1	nfsbc1 2950	1 ⊢ Ⅎ𝑥[𝐴 / 𝑥]𝜑

Syntax hints:  Ⅎwnf 1437  [wsbc 2933

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1481  ax-11 1483  ax-4 1487  ax-17 1503  ax-i9 1507  ax-ial 1511  ax-i5r 1512  ax-ext 2136

This theorem depends on definitions:  df-bi 116  df-tru 1335  df-nf 1438  df-sb 1740  df-clab 2141  df-cleq 2147  df-clel 2150  df-nfc 2285  df-sbc 2934

This theorem is referenced by:  elrabsf  2971  cbvralcsf  3089  cbvrexcsf  3090  euotd  4209  findes  4556  omsinds  4575  elfvmptrab1  5555  ralrnmpt  5602  rexrnmpt  5603  dfopab2  6127  dfoprab3s  6128  mpoxopoveq  6177  findcard2  6823  findcard2s  6824  ac6sfi  6832  indpi  7241  nn0ind-raph  9260  uzind4s  9480  indstr  9483  fzrevral  9985  exfzdc  10117  uzsinds  10319  zsupcllemstep  11805  infssuzex  11809  prmind2  11968  bj-bdfindes  13462  bj-findes  13494