Theorem equcomd 2026

Description: Deduction form of equcom 2025, symmetry of equality. For the versions for classes, see eqcom 2747 and eqcomd 2746. (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 219	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 1802  ax-4 1816  ax-5 1917  ax-6 1974  ax-7 2015

This theorem depends on definitions:  df-bi 208  df-an 397  df-ex 1787

This theorem is referenced by:  sndisj  5071  fsumcom2  15734  fprodcom2  15947  catideu  17639  pospo  18307  dprdfcntz  19990  ordtt1  23369  eengtrkg  29080  cusgrfilem2  29550  frgr2wwlk1  30424  ssmxidl  33564  gonar  35630  bj-nfcsym  37259  exidu1  38230  rngoideu  38277  2reu8i  47583  ichnreuop  47954  sprsymrelf1lem  47973  oppcthinendcALT  49938