Theorem nfsbc1v 2776

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 2175	. 2 ⊢ ℲxA
2	1	nfsbc1 2775	1 ⊢ Ⅎx[A / x]φ

Syntax hints:  Ⅎwnf 1346  [wsbc 2758

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 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-11 1394  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019

This theorem depends on definitions:  df-bi 110  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-sbc 2759

This theorem is referenced by:  elrabsf  2795  cbvralcsf  2902  cbvrexcsf  2903  euotd  3982  findes  4269  ralrnmpt  5252  rexrnmpt  5253  dfopab2  5757  dfoprab3s  5758  mpt2xopoveq  5796  indpi  6326  nn0ind-raph  8131  uzind4s  8309  indstr  8312  fzrevral  8737  bj-bdfindes  9409  bj-findes  9441