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Theorem 2sb6rf 2196
 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 2168 . 2
3 19.21v 1914 . . . 4
4 sbcom2 2191 . . . . . . 7
54imbi2i 305 . . . . . 6
6 impexp 435 . . . . . 6
75, 6bitri 242 . . . . 5
87albii 1576 . . . 4
9 2sb5rf.2 . . . . . . 7
109nfsb 2186 . . . . . 6
1110sb6rf 2168 . . . . 5
1211imbi2i 305 . . . 4
133, 8, 123bitr4ri 271 . . 3
1413albii 1576 . 2
152, 14bitri 242 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 178   wa 360  wal 1550  wnf 1554  wsb 1659 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-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660
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