Theorem nfsbc1v 2983

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 2982	1 ⊢ Ⅎ𝑥[𝐴 / 𝑥]𝜑

Syntax hints:  Ⅎwnf 1460  [wsbc 2964

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 2965

This theorem is referenced by:  elrabsf  3003  cbvralcsf  3121  cbvrexcsf  3122  euotd  4256  findes  4604  omsinds  4623  elfvmptrab1  5612  ralrnmpt  5660  rexrnmpt  5661  dfopab2  6192  dfoprab3s  6193  mpoxopoveq  6243  findcard2  6891  findcard2s  6892  ac6sfi  6900  dcfi  6982  indpi  7343  nn0ind-raph  9372  uzind4s  9592  indstr  9595  fzrevral  10107  exfzdc  10242  uzsinds  10444  zsupcllemstep  11948  infssuzex  11952  prmind2  12122  bj-bdfindes  14740  bj-findes  14772