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Theorem equcomd 2116
Description: Deduction form of equcom 2115, symmetry of equality. For the versions for classes, see eqcom 2772 and eqcomd 2771. (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 2115 . 2 (𝑥 = 𝑦𝑦 = 𝑥)
31, 2sylib 209 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 1890  ax-4 1904  ax-5 2005  ax-6 2070  ax-7 2105
This theorem depends on definitions:  df-bi 198  df-an 385  df-ex 1875
This theorem is referenced by:  sndisj  4801  fsumcom2  14790  fprodcom2  14997  catideu  16601  cusgrfilem2  26643  frgr2wwlk1  27609  bj-ssbequ1  33080  bj-nfcsym  33311  exidu1  34077  rngoideu  34124  sprsymrelf1lem  42410
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