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Theorem 2sb5 2292
 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 2279 . 2
2 19.42v 1842 . . . 4
3 anass 661 . . . . 5
43exbii 1726 . . . 4
5 sb5 2279 . . . . 5
65anbi2i 708 . . . 4
72, 4, 63bitr4ri 286 . . 3
87exbii 1726 . 2
91, 8bitri 257 1
 Colors of variables: wff setvar class Syntax hints:   wb 189   wa 376  wex 1671  wsb 1805 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1677  ax-4 1690  ax-5 1766  ax-6 1813  ax-7 1859  ax-10 1932  ax-12 1950  ax-13 2104 This theorem depends on definitions:  df-bi 190  df-an 378  df-ex 1672  df-nf 1676  df-sb 1806 This theorem is referenced by:  opelopabsbALT  4710
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