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Theorem equcomd 2022
Description: Deduction form of equcom 2021, symmetry of equality. For the versions for classes, see eqcom 2745 and eqcomd 2744. (Contributed by BJ, 6-Oct-2019.)
Hypothesis
Ref Expression
equcomd.1 (𝜑𝑥 = 𝑦)
Assertion
Ref Expression
equcomd (𝜑𝑦 = 𝑥)

Proof of Theorem equcomd
StepHypRef Expression
1 equcomd.1 . 2 (𝜑𝑥 = 𝑦)
2 equcom 2021 . 2 (𝑥 = 𝑦𝑦 = 𝑥)
31, 2sylib 217 1 (𝜑𝑦 = 𝑥)
Colors of variables: wff setvar class
Syntax hints:  wi 4
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1913  ax-6 1971  ax-7 2011
This theorem depends on definitions:  df-bi 206  df-an 397  df-ex 1783
This theorem is referenced by:  sndisj  5065  fsumcom2  15486  fprodcom2  15694  catideu  17384  pospo  18063  dprdfcntz  19618  ordtt1  22530  eengtrkg  27354  cusgrfilem2  27823  frgr2wwlk1  28693  ssmxidl  31642  gonar  33357  bj-nfcsym  35084  exidu1  36014  rngoideu  36061  2reu8i  44605  ichnreuop  44924  sprsymrelf1lem  44943
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