Theorem equcomd 2014

Description: Deduction form of equcom 2013, symmetry of equality. For the versions for classes, see eqcom 2731 and eqcomd 2730. (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 2013	. 2 ⊢ (𝑥 = 𝑦 ↔ 𝑦 = 𝑥)
3	1, 2	sylib 217	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 1789  ax-4 1803  ax-5 1905  ax-6 1963  ax-7 2003

This theorem depends on definitions:  df-bi 206  df-an 396  df-ex 1774

This theorem is referenced by:  sndisj  5129  fsumcom2  15716  fprodcom2  15924  catideu  17615  pospo  18297  dprdfcntz  19922  ordtt1  23193  eengtrkg  28668  cusgrfilem2  29137  frgr2wwlk1  30006  ssmxidl  33021  gonar  34841  bj-nfcsym  36235  exidu1  37180  rngoideu  37227  2reu8i  46272  ichnreuop  46591  sprsymrelf1lem  46610