Theorem nfsbc1v 2955

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 2299	. 2 |- F/_ x A
2	1	nfsbc1 2954	1 |- F/ x [. A / x ]. ph

Syntax hints:   F/wnf 1440   [.wsbc 2937

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 1427  ax-7 1428  ax-gen 1429  ax-ie1 1473  ax-ie2 1474  ax-8 1484  ax-11 1486  ax-4 1490  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2139

This theorem depends on definitions:  df-bi 116  df-tru 1338  df-nf 1441  df-sb 1743  df-clab 2144  df-cleq 2150  df-clel 2153  df-nfc 2288  df-sbc 2938

This theorem is referenced by:  elrabsf  2975  cbvralcsf  3093  cbvrexcsf  3094  euotd  4213  findes  4560  omsinds  4579  elfvmptrab1  5559  ralrnmpt  5606  rexrnmpt  5607  dfopab2  6131  dfoprab3s  6132  mpoxopoveq  6181  findcard2  6827  findcard2s  6828  ac6sfi  6836  indpi  7245  nn0ind-raph  9264  uzind4s  9484  indstr  9487  fzrevral  9989  exfzdc  10121  uzsinds  10323  zsupcllemstep  11813  infssuzex  11817  prmind2  11977  bj-bdfindes  13483  bj-findes  13515