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Theorem frege54cor1c 36582
 Description: Reflexive equality. (Contributed by RP, 24-Dec-2019.) (Revised by RP, 25-Apr-2020.)
Hypothesis
Ref Expression
frege54c.1
Assertion
Ref Expression
frege54cor1c
Distinct variable group:   ,
Allowed substitution hint:   ()

Proof of Theorem frege54cor1c
StepHypRef Expression
1 frege54c.1 . . . . 5
21elexi 3041 . . . 4
32snid 3988 . . 3
4 df-sn 3960 . . 3
53, 4eleqtri 2547 . 2
6 df-sbc 3256 . 2
75, 6mpbir 214 1
 Colors of variables: wff setvar class Syntax hints:   wceq 1452   wcel 1904  cab 2457  wsbc 3255  csn 3959 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1677  ax-4 1690  ax-5 1766  ax-6 1813  ax-7 1859  ax-10 1932  ax-11 1937  ax-12 1950  ax-13 2104  ax-ext 2451 This theorem depends on definitions:  df-bi 190  df-an 378  df-tru 1455  df-ex 1672  df-nf 1676  df-sb 1806  df-clab 2458  df-cleq 2464  df-clel 2467  df-nfc 2601  df-v 3033  df-sbc 3256  df-sn 3960 This theorem is referenced by:  frege55lem2c  36584  frege55c  36585  frege56c  36586
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