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Theorem 2sb5 2112
 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 2100 . 2
2 19.42v 1905 . . . 4
3 anass 630 . . . . 5
43exbii 1582 . . . 4
5 sb5 2100 . . . . 5
65anbi2i 675 . . . 4
72, 4, 63bitr4ri 269 . . 3
87exbii 1582 . 2
91, 8bitri 240 1
 Colors of variables: wff setvar class Syntax hints:   wb 176   wa 358  wex 1541  wsb 1648 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925 This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649 This theorem is referenced by:  pm11.07  2115
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