Theorem nfsbc1v 3070

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 2392	. 2 ⊢ Ⅎ𝑥𝐴
2	1	nfsbc1 3069	1 ⊢ Ⅎ𝑥[𝐴 / 𝑥]𝜑

This proof depends on syntax axioms:  Ⅎwnf 1513  [wsbc 3051

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1500  ax-7 1501  ax-gen 1502  ax-ie1 1546  ax-ie2 1547  ax-8 1557  ax-11 1559  ax-4 1563  ax-17 1579  ax-i9 1583  ax-ial 1587  ax-i5r 1588  ax-ext 2220

This proof depends on definitions:  df-bi 117  df-tru 1405  df-nf 1514  df-sb 1816  df-clab 2225  df-cleq 2231  df-clel 2234  df-nfc 2381  df-sbc 3052

This theorem is used by:  elrabsf  3090  cbvralcsf  3210  cbvrexcsf  3211  rabsnifsb  3777  euotd  4395  findes  4750  omsinds  4769  elfvmptrab1  5801  ralrnmpt  5850  rexrnmpt  5851  elovmporab  6289  elovmporab1w  6290  uchoice  6371  dfopab2  6423  dfoprab3s  6424  mpoxopoveq  6511  findcard2  7193  findcard2s  7194  ac6sfi  7202  opabfi  7247  dcfi  7315  indpi  7709  nn0ind-raph  9763  uzind4s  9990  indstr  9993  fzrevral  10512  exfzdc  10659  zsupcllemstep  10662  infssuzex  10666  uzsinds  10881  prmind2  12898  gropd  16288  grstructd2dom  16289  bj-bdfindes  16975  bj-findes  17007