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Theorem 2sb5rf 2193
 Description: Reversed double substitution. (Contributed by NM, 3-Feb-2005.) (Revised by Mario Carneiro, 6-Oct-2016.)
Hypotheses
Ref Expression
2sb5rf.1
2sb5rf.2
Assertion
Ref Expression
2sb5rf
Distinct variable groups:   ,   ,   ,   ,
Allowed substitution hints:   (,,,)

Proof of Theorem 2sb5rf
StepHypRef Expression
1 2sb5rf.1 . . 3
21sb5rf 2165 . 2
3 19.42v 1928 . . . 4
4 sbcom2 2189 . . . . . . 7
54anbi2i 676 . . . . . 6
6 anass 631 . . . . . 6
75, 6bitri 241 . . . . 5
87exbii 1592 . . . 4
9 2sb5rf.2 . . . . . . 7
109nfsb 2184 . . . . . 6
1110sb5rf 2165 . . . . 5
1211anbi2i 676 . . . 4
133, 8, 123bitr4ri 270 . . 3
1413exbii 1592 . 2
152, 14bitri 241 1
 Colors of variables: wff set class Syntax hints:   wb 177   wa 359  wex 1550  wnf 1553  wsb 1658 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659
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