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Theorem 2sb5rfOLD7 29823
 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
2sb5rfOLD7
Distinct variable groups:   ,   ,   ,   ,
Allowed substitution hints:   (,,,)

Proof of Theorem 2sb5rfOLD7
StepHypRef Expression
1 2sb5rf.1OLD7 . . 3
21sb5rfNEW7 29653 . 2
3 19.42v 1929 . . . 4
4 sbcom2NEW7 29706 . . . . . . 7
54anbi2i 677 . . . . . 6
6 anass 632 . . . . . 6
75, 6bitri 242 . . . . 5
87exbii 1593 . . . 4
9 2sb5rf.2OLD7 . . . . . . 7
109nfsbOLD7 29810 . . . . . 6
1110sb5rfNEW7 29653 . . . . 5
1211anbi2i 677 . . . 4
133, 8, 123bitr4ri 271 . . 3
1413exbii 1593 . 2
152, 14bitri 242 1
 Colors of variables: wff set class Syntax hints:   wb 178   wa 360  wex 1551  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-11 1762  ax-12 1951  ax-7v 29504  ax-7OLD7 29740 This theorem depends on definitions:  df-bi 179  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660
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