Theorem equcomd 1731

Description: Deduction form of equcom 1730, symmetry of equality. For the versions for classes, see eqcom 2209 and eqcomd 2213. (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 1730	. 2 |- ( x = y <-> y = x )
3	1, 2	sylib 122	1 |- ( ph -> y = x )

Syntax hints:   -> wi 4

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-gen 1473  ax-ie2 1518  ax-8 1528  ax-17 1550  ax-i9 1554

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  fisumcom2  11864  fprodcom2fi  12052  trirec0  16185