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Theorem equcomd 1992
Description: Deduction form of equcom 1991, symmetry of equality. For the versions for classes, see eqcom 2658 and eqcomd 2657. (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 1991 . 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 1762  ax-4 1777  ax-5 1879  ax-6 1945  ax-7 1981
This theorem depends on definitions:  df-bi 197  df-an 385  df-ex 1745
This theorem is referenced by:  sndisj  4676  fsumcom2  14549  fprodcom2  14758  catideu  16383  cusgrfilem2  26408  frgr2wwlk1  27309  bj-ssbequ1  32769  bj-nfcsym  33011  sprsymrelf1lem  42066
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