Theorem equcomd 2018

Description: Deduction form of equcom 2017, 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 2017	. 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 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2007

This theorem depends on definitions:  df-bi 207  df-an 396  df-ex 1780

This theorem is referenced by:  sndisj  5111  fsumcom2  15790  fprodcom2  16000  catideu  17687  pospo  18355  dprdfcntz  19998  ordtt1  23317  eengtrkg  28965  cusgrfilem2  29436  frgr2wwlk1  30310  ssmxidl  33489  gonar  35417  bj-nfcsym  36917  exidu1  37880  rngoideu  37927  2reu8i  47142  ichnreuop  47486  sprsymrelf1lem  47505  oppcthinendcALT  49327