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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:   ,,   ,
Allowed substitution hints:   (,,,)

Proof of Theorem 2sb6
StepHypRef Expression
1 sb6 2174 . 2
2 19.21v 1913 . . . 4
3 impexp 434 . . . . 5
43albii 1575 . . . 4
5 sb6 2174 . . . . 5
65imbi2i 304 . . . 4
72, 4, 63bitr4ri 270 . . 3
87albii 1575 . 2
91, 8bitri 241 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wa 359  wal 1549  wsb 1658 This theorem is referenced by:  2eu6  2365 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 This theorem depends on definitions:  df-bi 178  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659
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