Theorem equcomd 2031

Description: Deduction form of equcom 2030, 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 2030	. 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 1802  ax-4 1816  ax-5 1917  ax-6 1975  ax-7 2020

This theorem depends on definitions:  df-bi 210  df-an 400  df-ex 1787

This theorem is referenced by:  sndisj  5021  fsumcom2  15222  fprodcom2  15430  catideu  17049  pospo  17699  dprdfcntz  19256  ordtt1  22130  eengtrkg  26932  cusgrfilem2  27398  frgr2wwlk1  28266  ssmxidl  31214  gonar  32928  bj-nfcsym  34728  exidu1  35657  rngoideu  35704  2reu8i  44158  ichnreuop  44478  sprsymrelf1lem  44497