Theorem nfsbc1v 2782

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 2178	. 2 ⊢ Ⅎ𝑥𝐴
2	1	nfsbc1 2781	1 ⊢ Ⅎ𝑥[𝐴 / 𝑥]𝜑

Syntax hints:  Ⅎwnf 1349  [wsbc 2764

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-11 1397  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022

This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-sbc 2765

This theorem is referenced by:  elrabsf  2801  cbvralcsf  2908  cbvrexcsf  2909  euotd  3991  findes  4326  ralrnmpt  5309  rexrnmpt  5310  dfopab2  5815  dfoprab3s  5816  mpt2xopoveq  5855  findcard2  6346  findcard2s  6347  ac6sfi  6352  indpi  6438  nn0ind-raph  8353  uzind4s  8531  indstr  8534  fzrevral  8965  bj-bdfindes  10048  bj-findes  10080