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Theorem nfbii 1338
Description: Equality theorem for not-free. (Contributed by Mario Carneiro, 11-Aug-2016.)
Hypothesis
Ref Expression
nfbii.1 (φψ)
Assertion
Ref Expression
nfbii (Ⅎxφ ↔ Ⅎxψ)

Proof of Theorem nfbii
StepHypRef Expression
1 nfbii.1 . . . 4 (φψ)
21albii 1335 . . . 4 (xφxψ)
31, 2imbi12i 228 . . 3 ((φxφ) ↔ (ψxψ))
43albii 1335 . 2 (x(φxφ) ↔ x(ψxψ))
5 df-nf 1326 . 2 (Ⅎxφx(φxφ))
6 df-nf 1326 . 2 (Ⅎxψx(ψxψ))
74, 5, 63bitr4i 201 1 (Ⅎxφ ↔ Ⅎxψ)
Colors of variables: wff set class
Syntax hints:  wi 4  wb 98  wal 1224  wnf 1325
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 1312  ax-gen 1314
This theorem depends on definitions:  df-bi 110  df-nf 1326
This theorem is referenced by:  nfxfr  1339  nfxfrd  1340  nfsb  1800  nfsbt  1828  hbsbd  1836  sbal1yz  1855  dvelimALT  1864  dvelimfv  1865  dvelimor  1872  nfeudv  1893  nfeuv  1896  nfceqi  2152  nfreudxy  2457  dfnfc2  3568
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