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Theorem equcomd 2022
Description: Deduction form of equcom 2021, symmetry of equality. For the versions for classes, see eqcom 2828 and eqcomd 2827. (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 220 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 1792  ax-4 1806  ax-5 1907  ax-6 1966  ax-7 2011
This theorem depends on definitions:  df-bi 209  df-an 399  df-ex 1777
This theorem is referenced by:  sndisj  5049  fsumcom2  15123  fprodcom2  15332  catideu  16940  pospo  17577  dprdfcntz  19131  ordtt1  21981  eengtrkg  26766  cusgrfilem2  27232  frgr2wwlk1  28102  ssmxidl  30974  gonar  32637  bj-nfcsym  34210  exidu1  35128  rngoideu  35175  2reu8i  43306  ichnreuop  43628  sprsymrelf1lem  43647
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