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Theorem 2sb6rf 2118
 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
2sb6rf
Distinct variable groups:   ,   ,   ,   ,
Allowed substitution hints:   (,,,)

Proof of Theorem 2sb6rf
StepHypRef Expression
1 2sb5rf.1 . . 3
21sb6rf 2091 . 2
3 19.21v 1890 . . . 4
4 sbcom2 2114 . . . . . . 7
54imbi2i 303 . . . . . 6
6 impexp 433 . . . . . 6
75, 6bitri 240 . . . . 5
87albii 1566 . . . 4
9 2sb5rf.2 . . . . . . 7
109nfsb 2109 . . . . . 6
1110sb6rf 2091 . . . . 5
1211imbi2i 303 . . . 4
133, 8, 123bitr4ri 269 . . 3
1413albii 1566 . 2
152, 14bitri 240 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 176   wa 358  wal 1540  wnf 1544  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: (None)
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