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Theorem 2sb6rfOLD7 29689
 Description: Reversed double substitution. (Contributed by NM, 3-Feb-2005.) (Revised by Mario Carneiro, 6-Oct-2016.)
Hypotheses
Ref Expression
2sb5rf.1OLD7
2sb5rf.2OLD7
Assertion
Ref Expression
2sb6rfOLD7
Distinct variable groups:   ,   ,   ,   ,
Allowed substitution hints:   (,,,)

Proof of Theorem 2sb6rfOLD7
StepHypRef Expression
1 2sb5rf.1OLD7 . . 3
21sb6rfNEW7 29519 . 2
3 19.21v 1913 . . . 4
4 sbcom2NEW7 29571 . . . . . . 7
54imbi2i 304 . . . . . 6
6 impexp 434 . . . . . 6
75, 6bitri 241 . . . . 5
87albii 1575 . . . 4
9 2sb5rf.2OLD7 . . . . . . 7
109nfsbOLD7 29675 . . . . . 6
1110sb6rfNEW7 29519 . . . . 5
1211imbi2i 304 . . . 4
133, 8, 123bitr4ri 270 . . 3
1413albii 1575 . 2
152, 14bitri 241 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wa 359  wal 1549  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-11 1761  ax-12 1950  ax-7v 29369  ax-7OLD7 29605 This theorem depends on definitions:  df-bi 178  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659
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