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Theorem sbc19.21g 3400
Description: Substitution for a variable not free in antecedent affects only the consequent. (Contributed by NM, 11-Oct-2004.)
Hypothesis
Ref Expression
sbcgf.1
Assertion
Ref Expression
sbc19.21g

Proof of Theorem sbc19.21g
StepHypRef Expression
1 sbcimg 3369 . 2
2 sbcgf.1 . . . 4
32sbcgf 3399 . . 3
43imbi1d 317 . 2
51, 4bitrd 253 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  <->wb 184  F/wnf 1616  e.wcel 1818  [.wsbc 3327
This theorem is referenced by:  bnj121  33928  bnj124  33929  bnj130  33932  bnj207  33939  bnj611  33976  bnj1000  33999
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-or 370  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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