Theorem nfsbc1v 3047

Description: Bound-variable hypothesis builder for class substitution. (Contributed by Mario Carneiro, 12-Oct-2016.)

Assertion

Ref	Expression
nfsbc1v	|- F/ x [. A / x ]. ph

Distinct variable group:   x, A

Allowed substitution hint:   ph( x)

Proof of Theorem nfsbc1v

Step	Hyp	Ref	Expression
1		nfcv 2372	. 2 |- F/_ x A
2	1	nfsbc1 3046	1 |- F/ x [. A / x ]. ph

Syntax hints:   F/wnf 1506   [.wsbc 3028

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 1493  ax-7 1494  ax-gen 1495  ax-ie1 1539  ax-ie2 1540  ax-8 1550  ax-11 1552  ax-4 1556  ax-17 1572  ax-i9 1576  ax-ial 1580  ax-i5r 1581  ax-ext 2211

This theorem depends on definitions:  df-bi 117  df-tru 1398  df-nf 1507  df-sb 1809  df-clab 2216  df-cleq 2222  df-clel 2225  df-nfc 2361  df-sbc 3029

This theorem is referenced by:  elrabsf  3067  cbvralcsf  3187  cbvrexcsf  3188  euotd  4342  findes  4696  omsinds  4715  elfvmptrab1  5734  ralrnmpt  5782  rexrnmpt  5783  elovmporab  6214  elovmporab1w  6215  uchoice  6292  dfopab2  6344  dfoprab3s  6345  mpoxopoveq  6397  findcard2  7064  findcard2s  7065  ac6sfi  7073  opabfi  7116  dcfi  7164  indpi  7545  nn0ind-raph  9580  uzind4s  9802  indstr  9805  fzrevral  10318  exfzdc  10463  zsupcllemstep  10466  infssuzex  10470  uzsinds  10683  prmind2  12663  gropd  15869  grstructd2dom  15870  bj-bdfindes  16421  bj-findes  16453