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Theorem equcomd 2104
Description: Deduction form of equcom 2103, symmetry of equality. For the versions for classes, see eqcom 2778 and eqcomd 2777. (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 2103 . 2 (𝑥 = 𝑦𝑦 = 𝑥)
31, 2sylib 208 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 1870  ax-4 1885  ax-5 1991  ax-6 2057  ax-7 2093
This theorem depends on definitions:  df-bi 197  df-an 383  df-ex 1853
This theorem is referenced by:  sndisj  4778  fsumcom2  14713  fprodcom2  14921  catideu  16543  cusgrfilem2  26587  frgr2wwlk1  27511  bj-ssbequ1  32981  bj-nfcsym  33215  sprsymrelf1lem  42269
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