Theorem equcomd 2017

Description: Deduction form of equcom 2016, symmetry of equality. For the versions for classes, see eqcom 2741 and eqcomd 2740. (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 2016	. 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 1794  ax-4 1808  ax-5 1909  ax-6 1966  ax-7 2006

This theorem depends on definitions:  df-bi 207  df-an 396  df-ex 1779

This theorem is referenced by:  sndisj  5115  fsumcom2  15793  fprodcom2  16003  catideu  17690  pospo  18360  dprdfcntz  20004  ordtt1  23334  eengtrkg  28932  cusgrfilem2  29403  frgr2wwlk1  30277  ssmxidl  33442  gonar  35375  bj-nfcsym  36875  exidu1  37838  rngoideu  37885  2reu8i  47098  ichnreuop  47432  sprsymrelf1lem  47451  oppcthinendcALT  49142