Theorem equcomd 2022

Description: Deduction form of equcom 2021, symmetry of equality. For the versions for classes, see eqcom 2828 and eqcomd 2827. (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 220	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 1792  ax-4 1806  ax-5 1907  ax-6 1966  ax-7 2011

This theorem depends on definitions:  df-bi 209  df-an 399  df-ex 1777

This theorem is referenced by:  sndisj  5056  fsumcom2  15128  fprodcom2  15337  catideu  16945  pospo  17582  dprdfcntz  19136  ordtt1  21986  eengtrkg  26771  cusgrfilem2  27237  frgr2wwlk1  28107  ssmxidl  30979  gonar  32642  bj-nfcsym  34215  exidu1  35133  rngoideu  35180  2reu8i  43311  ichnreuop  43633  sprsymrelf1lem  43652