Theorem equcomd 2021

Description: Deduction form of equcom 2020, symmetry of equality. For the versions for classes, see eqcom 2744 and eqcomd 2743. (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 2020	. 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 1797  ax-4 1811  ax-5 1912  ax-6 1969  ax-7 2010

This theorem depends on definitions:  df-bi 207  df-an 396  df-ex 1782

This theorem is referenced by:  sndisj  5092  fsumcom2  15709  fprodcom2  15919  catideu  17610  pospo  18278  dprdfcntz  19958  ordtt1  23335  eengtrkg  29071  cusgrfilem2  29542  frgr2wwlk1  30416  ssmxidl  33566  gonar  35608  bj-nfcsym  37144  exidu1  38104  rngoideu  38151  2reu8i  47470  ichnreuop  47829  sprsymrelf1lem  47848  oppcthinendcALT  49797