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Theorem cleqhOLD 2545
 Description: Obsolete proof of cleqh 2544 as of 14-Nov-2019. (Contributed by NM, 26-May-1993.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
cleqh.1
cleqh.2
Assertion
Ref Expression
cleqhOLD
Distinct variable groups:   ,   ,   ,
Allowed substitution hints:   ()   ()

Proof of Theorem cleqhOLD
StepHypRef Expression
1 dfcleq 2422 . 2
2 ax-5 1751 . . . 4
3 dfbi2 632 . . . . 5
4 cleqh.1 . . . . . . 7
5 cleqh.2 . . . . . . 7
64, 5hbim 1980 . . . . . 6
75, 4hbim 1980 . . . . . 6
86, 7hban 1989 . . . . 5
93, 8hbxfrbi 1690 . . . 4
10 eleq1 2501 . . . . . 6
11 eleq1 2501 . . . . . 6
1210, 11bibi12d 322 . . . . 5
1312biimpd 210 . . . 4
142, 9, 13cbv3h 2072 . . 3
1512equcoms 1847 . . . . 5
1615biimprd 226 . . . 4
179, 2, 16cbv3h 2072 . . 3
1814, 17impbii 190 . 2
191, 18bitr4i 255 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 187   wa 370  wal 1435   wceq 1437   wcel 1870 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1665  ax-4 1678  ax-5 1751  ax-6 1797  ax-7 1841  ax-10 1889  ax-11 1894  ax-12 1907  ax-13 2055  ax-ext 2407 This theorem depends on definitions:  df-bi 188  df-an 372  df-ex 1660  df-nf 1664  df-cleq 2421  df-clel 2424 This theorem is referenced by: (None)
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