Theorem equcomd 2049

Description: Deduction form of equcom 2048, symmetry of equality. For the versions for classes, see eqcom 2770 and eqcomd 2769. (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 2048	. 2 ⊢ (𝑥 = 𝑦 ↔ 𝑦 = 𝑥)
3	1, 2	sylib 221	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 1825  ax-4 1839  ax-5 1940  ax-6 1997  ax-7 2038

This theorem depends on definitions:  df-bi 210  df-an 401  df-ex 1810

This theorem is referenced by:  sndisj  5102  fsumcom2  15827  fprodcom2  16040  catideu  17732  pospo  18400  dprdfcntz  20088  ordtt1  23517  eengtrkg  29317  cusgrfilem2  29787  frgr2wwlk1  30661  ssmxidl  33738  gonar  35868  bj-nfcsym  37515  exidu1  38488  rngoideu  38535  2reu8i  47833  ichnreuop  48204  sprsymrelf1lem  48223  oppcthinendcALT  50202