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Theorem nfsbc1v 2759
Description: Bound-variable hypothesis builder for class substitution. (Contributed by Mario Carneiro, 12-Oct-2016.)
Assertion
Ref Expression
nfsbc1v x[A / x]φ
Distinct variable group:   x,A
Allowed substitution hint:   φ(x)

Proof of Theorem nfsbc1v
StepHypRef Expression
1 nfcv 2160 . 2 xA
21nfsbc1 2758 1 x[A / x]φ
Colors of variables: wff set class
Syntax hints:  wnf 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
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