Theorem nfsbc1v 2981

Description: Bound-variable hypothesis builder for class substitution. (Contributed by Mario Carneiro, 12-Oct-2016.)

Assertion

Ref	Expression
nfsbc1v	⊢ Ⅎ𝑥[𝐴 / 𝑥]𝜑

Distinct variable group:   𝑥,𝐴

Allowed substitution hint:   𝜑(𝑥)

Proof of Theorem nfsbc1v

Step	Hyp	Ref	Expression
1		nfcv 2319	. 2 ⊢ Ⅎ𝑥𝐴
2	1	nfsbc1 2980	1 ⊢ Ⅎ𝑥[𝐴 / 𝑥]𝜑

Syntax hints:  Ⅎwnf 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  4254  findes  4602  omsinds  4621  elfvmptrab1  5610  ralrnmpt  5658  rexrnmpt  5659  dfopab2  6189  dfoprab3s  6190  mpoxopoveq  6240  findcard2  6888  findcard2s  6889  ac6sfi  6897  dcfi  6979  indpi  7340  nn0ind-raph  9369  uzind4s  9589  indstr  9592  fzrevral  10104  exfzdc  10239  uzsinds  10441  zsupcllemstep  11945  infssuzex  11949  prmind2  12119  bj-bdfindes  14671  bj-findes  14703