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Theorem equcomd 1932
Description: Deduction form of equcom 1931, symmetry of equality. For the versions for classes, see eqcom 2616 and eqcomd 2615. (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 1931 . 2 (𝑥 = 𝑦𝑦 = 𝑥)
31, 2sylib 206 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 1712  ax-4 1727  ax-5 1826  ax-6 1874  ax-7 1921
This theorem depends on definitions:  df-bi 195  df-an 384  df-ex 1695
This theorem is referenced by:  sndisj  4568  fsumcom2  14293  fprodcom2  14499  cusgrafilem2  25774  bj-ssbequ1  31639  bj-nfcsym  31875  cusgrfilem2  40667
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