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Theorem 2sb5 1859
 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 1767 . 2
2 19.42v 1786 . . . 4
3 anass 381 . . . . 5
43exbii 1496 . . . 4
5 sb5 1767 . . . . 5
65anbi2i 430 . . . 4
72, 4, 63bitr4ri 202 . . 3
87exbii 1496 . 2
91, 8bitri 173 1
 Colors of variables: wff set class Syntax hints:   wa 97   wb 98  wex 1381  wsb 1645 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1336  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-11 1397  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427 This theorem depends on definitions:  df-bi 110  df-sb 1646 This theorem is referenced by:  opelopabsbALT  3996
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