Theorem nfsbc1v 2759

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 2160	. 2 ⊢ ℲxA
2	1	nfsbc1 2758	1 ⊢ Ⅎx[A / x]φ

Syntax hints:  Ⅎwnf 1329  [wsbc 2741

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 1316  ax-7 1317  ax-gen 1318  ax-ie1 1363  ax-ie2 1364  ax-8 1376  ax-11 1378  ax-4 1381  ax-17 1400  ax-i9 1404  ax-ial 1409  ax-i5r 1410  ax-ext 2004

This theorem depends on definitions:  df-bi 110  df-tru 1231  df-nf 1330  df-sb 1628  df-clab 2009  df-cleq 2015  df-clel 2018  df-nfc 2149  df-sbc 2742

This theorem is referenced by:  elrabsf  2778  cbvralcsf  2885  cbvrexcsf  2886  euotd  3965  findes  4253  ralrnmpt  5234  rexrnmpt  5235  dfopab2  5738  dfoprab3s  5739  mpt2xopoveq  5777  bj-bdfindes  7318  bj-findes  7346