Theorem equcomd 2021

Description: Deduction form of equcom 2020, symmetry of equality. For the versions for classes, see eqcom 2743 and eqcomd 2742. (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  5077  fsumcom2  15736  fprodcom2  15949  catideu  17641  pospo  18309  dprdfcntz  19992  ordtt1  23344  eengtrkg  29055  cusgrfilem2  29525  frgr2wwlk1  30399  ssmxidl  33534  gonar  35577  bj-nfcsym  37206  exidu1  38177  rngoideu  38224  2reu8i  47561  ichnreuop  47932  sprsymrelf1lem  47951  oppcthinendcALT  49916