Theorem nfsbc1v 2931

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 2282	. 2 |- F/_ x A
2	1	nfsbc1 2930	1 |- F/ x [. A / x ]. ph

Syntax hints:   F/wnf 1437   [.wsbc 2913

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 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-11 1485  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516  ax-ext 2122

This theorem depends on definitions:  df-bi 116  df-tru 1335  df-nf 1438  df-sb 1737  df-clab 2127  df-cleq 2133  df-clel 2136  df-nfc 2271  df-sbc 2914

This theorem is referenced by:  elrabsf  2951  cbvralcsf  3067  cbvrexcsf  3068  euotd  4184  findes  4525  omsinds  4543  elfvmptrab1  5523  ralrnmpt  5570  rexrnmpt  5571  dfopab2  6095  dfoprab3s  6096  mpoxopoveq  6145  findcard2  6791  findcard2s  6792  ac6sfi  6800  indpi  7174  nn0ind-raph  9192  uzind4s  9412  indstr  9415  fzrevral  9916  exfzdc  10048  uzsinds  10246  zsupcllemstep  11674  infssuzex  11678  prmind2  11837  bj-bdfindes  13318  bj-findes  13350