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Theorem 2sb6rf 1908
 Description: Reversed double substitution. (Contributed by NM, 3-Feb-2005.)
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 1775 . 2
3 19.21v 1795 . . . 4
4 sbcom2 1905 . . . . . . 7
54imbi2i 224 . . . . . 6
6 impexp 259 . . . . . 6
75, 6bitri 182 . . . . 5
87albii 1400 . . . 4
9 2sb5rf.2 . . . . . . 7
109hbsbv 1859 . . . . . 6
1110sb6rf 1775 . . . . 5
1211imbi2i 224 . . . 4
133, 8, 123bitr4ri 211 . . 3
1413albii 1400 . 2
152, 14bitri 182 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 102   wb 103  wal 1283  wsb 1686 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469 This theorem depends on definitions:  df-bi 115  df-nf 1391  df-sb 1687 This theorem is referenced by: (None)
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