Theorem nfsbc1v 3018

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 2349	. 2 |- F/_ x A
2	1	nfsbc1 3017	1 |- F/ x [. A / x ]. ph

Syntax hints:   F/wnf 1484   [.wsbc 2999

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 1471  ax-7 1472  ax-gen 1473  ax-ie1 1517  ax-ie2 1518  ax-8 1528  ax-11 1530  ax-4 1534  ax-17 1550  ax-i9 1554  ax-ial 1558  ax-i5r 1559  ax-ext 2188

This theorem depends on definitions:  df-bi 117  df-tru 1376  df-nf 1485  df-sb 1787  df-clab 2193  df-cleq 2199  df-clel 2202  df-nfc 2338  df-sbc 3000

This theorem is referenced by:  elrabsf  3038  cbvralcsf  3157  cbvrexcsf  3158  euotd  4303  findes  4655  omsinds  4674  elfvmptrab1  5681  ralrnmpt  5729  rexrnmpt  5730  elovmporab  6153  elovmporab1w  6154  uchoice  6230  dfopab2  6282  dfoprab3s  6283  mpoxopoveq  6333  findcard2  6993  findcard2s  6994  ac6sfi  7002  opabfi  7042  dcfi  7090  indpi  7462  nn0ind-raph  9497  uzind4s  9718  indstr  9721  fzrevral  10234  exfzdc  10376  zsupcllemstep  10379  infssuzex  10383  uzsinds  10596  prmind2  12486  gropd  15690  grstructd2dom  15691  bj-bdfindes  15959  bj-findes  15991