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Theorem 2sb6 2188
Description: Equivalence for double substitution. (Contributed by NM, 3-Feb-2005.)
Assertion
Ref Expression
2sb6
Distinct variable groups:   , ,   ,

Proof of Theorem 2sb6
StepHypRef Expression
1 sb6 2173 . 2
2 19.21v 1729 . . . 4
3 impexp 446 . . . . 5
43albii 1640 . . . 4
5 sb6 2173 . . . . 5
65imbi2i 312 . . . 4
72, 4, 63bitr4ri 278 . . 3
87albii 1640 . 2
91, 8bitri 249 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  <->wb 184  /\wa 369  A.wal 1393  [wsb 1739
This theorem is referenced by:  sbcom2  2189  2exsb  2213  2moOLD  2374  2eu6  2383  2eu6OLD  2384
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-an 371  df-ex 1613  df-nf 1617  df-sb 1740
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