Theorem equcomd 2020

Description: Deduction form of equcom 2019, symmetry of equality. For the versions for classes, see eqcom 2740 and eqcomd 2739. (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 2019	. 2 ⊢ (𝑥 = 𝑦 ↔ 𝑦 = 𝑥)
3	1, 2	sylib 218	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 1796  ax-4 1810  ax-5 1911  ax-6 1968  ax-7 2009

This theorem depends on definitions:  df-bi 207  df-an 396  df-ex 1781

This theorem is referenced by:  sndisj  5087  fsumcom2  15685  fprodcom2  15895  catideu  17585  pospo  18253  dprdfcntz  19933  ordtt1  23297  eengtrkg  28968  cusgrfilem2  29439  frgr2wwlk1  30313  ssmxidl  33448  gonar  35462  bj-nfcsym  36966  exidu1  37919  rngoideu  37966  2reu8i  47240  ichnreuop  47599  sprsymrelf1lem  47618  oppcthinendcALT  49569