Theorem equcomd 2023

Description: Deduction form of equcom 2022, symmetry of equality. For the versions for classes, see eqcom 2745 and eqcomd 2744. (Contributed by BJ, 6-Oct-2019.)

Hypothesis

Ref	Expression
equcomd.1	⊢ (𝜑 → 𝑥 = 𝑦)

Assertion

Ref	Expression
equcomd	⊢ (𝜑 → 𝑦 = 𝑥)

Proof of Theorem equcomd

Step	Hyp	Ref	Expression
1		equcomd.1	. 2 ⊢ (𝜑 → 𝑥 = 𝑦)
2		equcom 2022	. 2 ⊢ (𝑥 = 𝑦 ↔ 𝑦 = 𝑥)
3	1, 2	sylib 217	1 ⊢ (𝜑 → 𝑦 = 𝑥)

Syntax hints:   → wi 4

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1799  ax-4 1813  ax-5 1914  ax-6 1972  ax-7 2012

This theorem depends on definitions:  df-bi 206  df-an 396  df-ex 1784

This theorem is referenced by:  sndisj  5061  fsumcom2  15414  fprodcom2  15622  catideu  17301  pospo  17978  dprdfcntz  19533  ordtt1  22438  eengtrkg  27257  cusgrfilem2  27726  frgr2wwlk1  28594  ssmxidl  31544  gonar  33257  bj-nfcsym  35011  exidu1  35941  rngoideu  35988  2reu8i  44492  ichnreuop  44812  sprsymrelf1lem  44831