Theorem equcomd 2038

Description: Deduction form of equcom 2037, symmetry of equality. For the versions for classes, see eqcom 2768 and eqcomd 2767. (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 2037	. 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 1814  ax-4 1828  ax-5 1929  ax-6 1986  ax-7 2027

This theorem depends on definitions:  df-bi 209  df-an 400  df-ex 1799

This theorem is referenced by:  sndisj  5089  fsumcom2  15791  fprodcom2  16004  catideu  17697  pospo  18365  dprdfcntz  20047  ordtt1  23426  eengtrkg  29143  cusgrfilem2  29613  frgr2wwlk1  30487  ssmxidl  33622  gonar  35705  bj-nfcsym  37344  exidu1  38315  rngoideu  38362  2reu8i  47667  ichnreuop  48038  sprsymrelf1lem  48057  oppcthinendcALT  50022