Theorem equcomd 2016

Description: Deduction form of equcom 2015, symmetry of equality. For the versions for classes, see eqcom 2742 and eqcomd 2741. (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 2015	. 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 1792  ax-4 1806  ax-5 1908  ax-6 1965  ax-7 2005

This theorem depends on definitions:  df-bi 207  df-an 396  df-ex 1777

This theorem is referenced by:  sndisj  5140  fsumcom2  15807  fprodcom2  16017  catideu  17720  pospo  18403  dprdfcntz  20050  ordtt1  23403  eengtrkg  29016  cusgrfilem2  29489  frgr2wwlk1  30358  ssmxidl  33482  gonar  35380  bj-nfcsym  36882  exidu1  37843  rngoideu  37890  2reu8i  47063  ichnreuop  47397  sprsymrelf1lem  47416