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Theorem sbbid 2144
 Description: Deduction substituting both sides of a biconditional. (Contributed by NM, 30-Jun-1993.)
Hypotheses
Ref Expression
sbbid.1
sbbid.2
Assertion
Ref Expression
sbbid

Proof of Theorem sbbid
StepHypRef Expression
1 sbbid.1 . . 3
2 sbbid.2 . . 3
31, 2alrimi 1877 . 2
4 spsbbi 2143 . 2
53, 4syl 16 1
 Colors of variables: wff setvar class Syntax hints:  ->wi 4  <->wb 184  A.wal 1393  F/wnf 1616  [wsb 1739 This theorem is referenced by:  sbcom3  2153  sbco3  2160  sbcom2  2189  sbal  2206  wl-equsb3  30004  wl-sbcom2d-lem1  30009  wl-sbcom3  30035 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 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-ex 1613  df-nf 1617  df-sb 1740
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