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Theorem 2sb6 1902
 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 1808 . 2
2 19.21v 1795 . . . 4
3 impexp 259 . . . . 5
43albii 1400 . . . 4
5 sb6 1808 . . . . 5
65imbi2i 224 . . . 4
72, 4, 63bitr4ri 211 . . 3
87albii 1400 . 2
91, 8bitri 182 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 102   wb 103  wal 1283  wsb 1686 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1377  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-11 1438  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469 This theorem depends on definitions:  df-bi 115  df-sb 1687 This theorem is referenced by: (None)
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