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Theorem 2sb5 2190
 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 2178 . 2
2 19.42v 1929 . . . 4
3 anass 632 . . . . 5
43exbii 1593 . . . 4
5 sb5 2178 . . . . 5
65anbi2i 677 . . . 4
72, 4, 63bitr4ri 271 . . 3
87exbii 1593 . 2
91, 8bitri 242 1
 Colors of variables: wff set class Syntax hints:   wb 178   wa 360  wex 1551  wsb 1659 This theorem is referenced by:  pm11.07OLD  2194  opelopabsbOLD  4465 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951 This theorem depends on definitions:  df-bi 179  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660
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