Theorem equcomd 2042

Description: Deduction form of equcom 2041, symmetry of equality. For the versions for classes, see eqcom 2772 and eqcomd 2771. (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 2041	. 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 1818  ax-4 1832  ax-5 1933  ax-6 1990  ax-7 2031

This theorem depends on definitions:  df-bi 210  df-an 401  df-ex 1803

This theorem is referenced by:  sndisj  5096  fsumcom2  15813  fprodcom2  16026  catideu  17719  pospo  18387  dprdfcntz  20075  ordtt1  23493  eengtrkg  29241  cusgrfilem2  29711  frgr2wwlk1  30585  ssmxidl  33669  gonar  35753  bj-nfcsym  37391  exidu1  38362  rngoideu  38409  2reu8i  47706  ichnreuop  48077  sprsymrelf1lem  48096  oppcthinendcALT  50071