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Theorem 2sb6rf 2251
 Description: Reversed double substitution. (Contributed by NM, 3-Feb-2005.) (Revised by Mario Carneiro, 6-Oct-2016.) Remove variable constraints. (Revised by Wolf Lammen, 28-Sep-2018.)
Hypotheses
Ref Expression
2sb5rf.1
2sb5rf.2
Assertion
Ref Expression
2sb6rf
Distinct variable group:   ,
Allowed substitution hints:   (,,,)

Proof of Theorem 2sb6rf
StepHypRef Expression
1 sbequ12r 2052 . . . . 5
2 sbequ12r 2052 . . . . 5
31, 2sylan9bb 704 . . . 4
43pm5.74i 248 . . 3
542albii 1686 . 2
6 2sb5rf.2 . . . . 5
7619.23 1970 . . . 4
87albii 1685 . . 3
9 2sb5rf.1 . . . 4
10919.23 1970 . . 3
118, 10bitri 252 . 2
12 2ax6e 2249 . . 3
13 pm5.5 337 . . 3
1412, 13ax-mp 5 . 2
155, 11, 143bitrri 275 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 187   wa 370  wal 1435  wex 1657  wnf 1661  wsb 1790 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1663  ax-4 1676  ax-5 1752  ax-6 1798  ax-7 1843  ax-10 1891  ax-11 1896  ax-12 1909  ax-13 2057 This theorem depends on definitions:  df-bi 188  df-an 372  df-ex 1658  df-nf 1662  df-sb 1791 This theorem is referenced by: (None)
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