Theorem nfsbc1v 2833

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 2219	. 2 ⊢ Ⅎ𝑥𝐴
2	1	nfsbc1 2832	1 ⊢ Ⅎ𝑥[𝐴 / 𝑥]𝜑

Syntax hints:  Ⅎwnf 1389  [wsbc 2815

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 1376  ax-7 1377  ax-gen 1378  ax-ie1 1422  ax-ie2 1423  ax-8 1435  ax-11 1437  ax-4 1440  ax-17 1459  ax-i9 1463  ax-ial 1467  ax-i5r 1468  ax-ext 2063

This theorem depends on definitions:  df-bi 115  df-tru 1287  df-nf 1390  df-sb 1686  df-clab 2068  df-cleq 2074  df-clel 2077  df-nfc 2208  df-sbc 2816

This theorem is referenced by:  elrabsf  2852  cbvralcsf  2964  cbvrexcsf  2965  euotd  4009  findes  4344  ralrnmpt  5330  rexrnmpt  5331  dfopab2  5835  dfoprab3s  5836  mpt2xopoveq  5878  findcard2  6373  findcard2s  6374  ac6sfi  6379  indpi  6532  nn0ind-raph  8464  uzind4s  8678  indstr  8681  fzrevral  9122  exfzdc  9249  uzsinds  9428  zsupcllemstep  10341  infssuzex  10345  prmind2  10502  bj-bdfindes  10744  bj-findes  10776