Theorem nfsbc1v 2834

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 2220	. 2 ⊢ Ⅎ𝑥𝐴
2	1	nfsbc1 2833	1 ⊢ Ⅎ𝑥[𝐴 / 𝑥]𝜑

Syntax hints:  Ⅎwnf 1390  [wsbc 2816

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-11 1438  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2064

This theorem depends on definitions:  df-bi 115  df-tru 1288  df-nf 1391  df-sb 1687  df-clab 2069  df-cleq 2075  df-clel 2078  df-nfc 2209  df-sbc 2817

This theorem is referenced by:  elrabsf  2853  cbvralcsf  2965  cbvrexcsf  2966  euotd  4017  findes  4352  ralrnmpt  5341  rexrnmpt  5342  dfopab2  5846  dfoprab3s  5847  mpt2xopoveq  5889  findcard2  6423  findcard2s  6424  ac6sfi  6431  indpi  6594  nn0ind-raph  8545  uzind4s  8759  indstr  8762  fzrevral  9198  exfzdc  9326  uzsinds  9518  zsupcllemstep  10485  infssuzex  10489  prmind2  10646  bj-bdfindes  10902  bj-findes  10934