Theorem equcomd 2026

Description: Deduction form of equcom 2025, symmetry of equality. For the versions for classes, see eqcom 2830 and eqcomd 2829. (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 2025	. 2 ⊢ (𝑥 = 𝑦 ↔ 𝑦 = 𝑥)
3	1, 2	sylib 220	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 1970  ax-7 2015

This theorem depends on definitions:  df-bi 209  df-an 399  df-ex 1781

This theorem is referenced by:  sndisj  5059  fsumcom2  15131  fprodcom2  15340  catideu  16948  pospo  17585  dprdfcntz  19139  ordtt1  21989  eengtrkg  26774  cusgrfilem2  27240  frgr2wwlk1  28110  ssmxidl  30981  gonar  32644  bj-nfcsym  34217  exidu1  35136  rngoideu  35183  2reu8i  43319  ichnreuop  43641  sprsymrelf1lem  43660