Theorem nfsbc1v 2982

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 2319	. 2 |- F/_ x A
2	1	nfsbc1 2981	1 |- F/ x [. A / x ]. ph

Syntax hints:   F/wnf 1460   [.wsbc 2963

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 1447  ax-7 1448  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-8 1504  ax-11 1506  ax-4 1510  ax-17 1526  ax-i9 1530  ax-ial 1534  ax-i5r 1535  ax-ext 2159

This theorem depends on definitions:  df-bi 117  df-tru 1356  df-nf 1461  df-sb 1763  df-clab 2164  df-cleq 2170  df-clel 2173  df-nfc 2308  df-sbc 2964

This theorem is referenced by:  elrabsf  3002  cbvralcsf  3120  cbvrexcsf  3121  euotd  4255  findes  4603  omsinds  4622  elfvmptrab1  5611  ralrnmpt  5659  rexrnmpt  5660  dfopab2  6190  dfoprab3s  6191  mpoxopoveq  6241  findcard2  6889  findcard2s  6890  ac6sfi  6898  dcfi  6980  indpi  7341  nn0ind-raph  9370  uzind4s  9590  indstr  9593  fzrevral  10105  exfzdc  10240  uzsinds  10442  zsupcllemstep  11946  infssuzex  11950  prmind2  12120  bj-bdfindes  14704  bj-findes  14736