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Theorem sbctt 3398
 Description: Substitution for a variable not free in a wff does not affect it. (Contributed by Mario Carneiro, 14-Oct-2016.)
Assertion
Ref Expression
sbctt

Proof of Theorem sbctt
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 dfsbcq2 3330 . . . . 5
21bibi1d 319 . . . 4
32imbi2d 316 . . 3
4 sbft 2120 . . 3
53, 4vtoclg 3167 . 2
65imp 429 1
 Colors of variables: wff setvar class Syntax hints:  ->wi 4  <->wb 184  /\wa 369  =wceq 1395  F/wnf 1616  [wsb 1739  e.wcel 1818  [.wsbc 3327 This theorem is referenced by:  sbcgf  3399  csbtt  3445 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-12 1854  ax-13 1999  ax-ext 2435 This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-v 3111  df-sbc 3328
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