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Theorem sbctt 3215
 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 3156 . . . . 5
21bibi1d 311 . . . 4
32imbi2d 308 . . 3
4 sbft 2103 . . 3
53, 4vtoclg 3003 . 2
65imp 419 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wa 359  wnf 1553   wceq 1652  wsb 1658   wcel 1725  wsbc 3153 This theorem is referenced by:  sbcgf  3216  csbtt  3255 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-v 2950  df-sbc 3154
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