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Theorem 2sb5rf 2069
 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 2043 . 2
3 19.42v 1858 . . . 4
4 sbcom2 2066 . . . . . . 7
54anbi2i 675 . . . . . 6
6 anass 630 . . . . . 6
75, 6bitri 240 . . . . 5
87exbii 1572 . . . 4
9 2sb5rf.2 . . . . . . 7
109nfsb 2061 . . . . . 6
1110sb5rf 2043 . . . . 5
1211anbi2i 675 . . . 4
133, 8, 123bitr4ri 269 . . 3
1413exbii 1572 . 2
152, 14bitri 240 1
 Colors of variables: wff set class Syntax hints:   wb 176   wa 358  wex 1531  wnf 1534  wsb 1638 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878 This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639
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