Theorem equcomd 1946

Description: Deduction form of equcom 1945, symmetry of equality. For the versions for classes, see eqcom 2629 and eqcomd 2628. (Contributed by BJ, 6-Oct-2019.)

Hypothesis

Ref	Expression
equcomd.1	|- ( ph -> x = y )

Assertion

Ref	Expression
equcomd	|- ( ph -> y = x )

Proof of Theorem equcomd

Step	Hyp	Ref	Expression
1		equcomd.1	. 2 |- ( ph -> x = y )
2		equcom 1945	. 2 |- ( x = y <-> y = x )
3	1, 2	sylib 208	1 |- ( ph -> 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 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935

This theorem depends on definitions:  df-bi 197  df-an 386  df-ex 1705

This theorem is referenced by:  sndisj  4644  fsumcom2  14505  fprodcom2  14714  catideu  16336  cusgrfilem2  26352  frgr2wwlk1  27193  bj-ssbequ1  32644  bj-nfcsym  32886  sprsymrelf1lem  41741