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Theorem 2sb5 2064
 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 2052 . 2
2 19.42v 1858 . . . 4
3 anass 630 . . . . 5
43exbii 1572 . . . 4
5 sb5 2052 . . . . 5
65anbi2i 675 . . . 4
72, 4, 63bitr4ri 269 . . 3
87exbii 1572 . 2
91, 8bitri 240 1
 Colors of variables: wff set class Syntax hints:   wb 176   wa 358  wex 1531  wsb 1638 This theorem is referenced by:  pm11.07  2067  opelopabsbOLD  4289 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878 This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639
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