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Theorem 2sb5 1959
 Description: Equivalence for double substitution. (Contributed by NM, 3-Feb-2005.)
Assertion
Ref Expression
2sb5
Distinct variable groups:   ,,   ,
Allowed substitution hints:   (,,,)

Proof of Theorem 2sb5
StepHypRef Expression
1 sb5 1860 . 2
2 19.42v 1879 . . . 4
3 anass 399 . . . . 5
43exbii 1585 . . . 4
5 sb5 1860 . . . . 5
65anbi2i 453 . . . 4
72, 4, 63bitr4ri 212 . . 3
87exbii 1585 . 2
91, 8bitri 183 1
 Colors of variables: wff set class Syntax hints:   wa 103   wb 104  wex 1469  wsb 1736 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1424  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-11 1485  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515 This theorem depends on definitions:  df-bi 116  df-sb 1737 This theorem is referenced by:  opelopabsbALT  4185
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