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Theorem frege55lem1c 38133
 Description: Necessary deduction regarding substitution of value in equality. (Contributed by RP, 24-Dec-2019.)
Assertion
Ref Expression
frege55lem1c
Distinct variable groups:   ,   ,
Allowed substitution hint:   ()

Proof of Theorem frege55lem1c
StepHypRef Expression
1 df-sbc 3328 . . 3
2 ax-frege1 38003 . . . . 5
3 eqeq1 2461 . . . . . 6
43elab3g 3252 . . . . 5
52, 4syl 16 . . . 4
65ibi 241 . . 3
71, 6sylbi 195 . 2
87imim2i 14 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 184   wceq 1395   wcel 1819  cab 2442  wsbc 3327 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1619  ax-4 1632  ax-5 1705  ax-6 1748  ax-7 1791  ax-10 1838  ax-11 1843  ax-12 1855  ax-13 2000  ax-ext 2435  ax-frege1 38003 This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1398  df-ex 1614  df-nf 1618  df-sb 1741  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-v 3111  df-sbc 3328 This theorem is referenced by:  frege56c  38136
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