Theorem equcomd 2026

Description: Deduction form of equcom 2025, symmetry of equality. For the versions for classes, see eqcom 2805 and eqcomd 2804. (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 221	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 1797  ax-4 1811  ax-5 1911  ax-6 1970  ax-7 2015

This theorem depends on definitions:  df-bi 210  df-an 400  df-ex 1782

This theorem is referenced by:  sndisj  5021  fsumcom2  15121  fprodcom2  15330  catideu  16938  pospo  17575  dprdfcntz  19130  ordtt1  21984  eengtrkg  26780  cusgrfilem2  27246  frgr2wwlk1  28114  ssmxidl  31050  gonar  32755  bj-nfcsym  34339  exidu1  35294  rngoideu  35341  2reu8i  43669  ichnreuop  43989  sprsymrelf1lem  44008