Theorem nfsbc1v 2981

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 2980	1 |- F/ x [. A / x ]. ph

Syntax hints:   F/wnf 1460   [.wsbc 2962

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 2963

This theorem is referenced by:  elrabsf  3001  cbvralcsf  3119  cbvrexcsf  3120  euotd  4253  findes  4601  omsinds  4620  elfvmptrab1  5609  ralrnmpt  5657  rexrnmpt  5658  dfopab2  6187  dfoprab3s  6188  mpoxopoveq  6238  findcard2  6886  findcard2s  6887  ac6sfi  6895  dcfi  6977  indpi  7338  nn0ind-raph  9366  uzind4s  9586  indstr  9589  fzrevral  10100  exfzdc  10235  uzsinds  10437  zsupcllemstep  11938  infssuzex  11942  prmind2  12112  bj-bdfindes  14561  bj-findes  14593