Theorem nfsbc1v 3051

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 2375	. 2 |- F/_ x A
2	1	nfsbc1 3050	1 |- F/ x [. A / x ]. ph

Syntax hints:   F/wnf 1509   [.wsbc 3032

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 1496  ax-7 1497  ax-gen 1498  ax-ie1 1542  ax-ie2 1543  ax-8 1553  ax-11 1555  ax-4 1559  ax-17 1575  ax-i9 1579  ax-ial 1583  ax-i5r 1584  ax-ext 2213

This theorem depends on definitions:  df-bi 117  df-tru 1401  df-nf 1510  df-sb 1811  df-clab 2218  df-cleq 2224  df-clel 2227  df-nfc 2364  df-sbc 3033

This theorem is referenced by:  elrabsf  3071  cbvralcsf  3191  cbvrexcsf  3192  rabsnifsb  3741  euotd  4353  findes  4707  omsinds  4726  elfvmptrab1  5750  ralrnmpt  5797  rexrnmpt  5798  elovmporab  6232  elovmporab1w  6233  uchoice  6309  dfopab2  6361  dfoprab3s  6362  mpoxopoveq  6449  findcard2  7121  findcard2s  7122  ac6sfi  7130  opabfi  7175  dcfi  7223  indpi  7605  nn0ind-raph  9641  uzind4s  9868  indstr  9871  fzrevral  10385  exfzdc  10532  zsupcllemstep  10535  infssuzex  10539  uzsinds  10752  prmind2  12755  gropd  15971  grstructd2dom  15972  bj-bdfindes  16648  bj-findes  16680