Theorem equcomd 2022

Description: Deduction form of equcom 2021, 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 2021	. 2 ⊢ (𝑥 = 𝑦 ↔ 𝑦 = 𝑥)
3	1, 2	sylib 217	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 1798  ax-4 1812  ax-5 1913  ax-6 1971  ax-7 2011

This theorem depends on definitions:  df-bi 206  df-an 397  df-ex 1783

This theorem is referenced by:  sndisj  5065  fsumcom2  15486  fprodcom2  15694  catideu  17384  pospo  18063  dprdfcntz  19618  ordtt1  22530  eengtrkg  27354  cusgrfilem2  27823  frgr2wwlk1  28693  ssmxidl  31642  gonar  33357  bj-nfcsym  35084  exidu1  36014  rngoideu  36061  2reu8i  44605  ichnreuop  44924  sprsymrelf1lem  44943