Theorem eqcomb 812

Description: Commutative law for equality.

Assertion

Ref	Expression
eqcomb	|- (x = y <-> y = x)

Proof of Theorem eqcomb

Step	Hyp	Ref	Expression
1		eqcom 811	. 2 |- (x = y -> y = x)
2		eqcom 811	. 2 |- (y = x -> x = y)
3	1, 2	impbi 139	1 |- (x = y <-> y = x)

Syntax hints:   <-> wb 127   = weq 797

This theorem is referenced by:  sbequ12r 866  eu1 1019  mapsnen 3334  znnen 4930

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6  ax-4 673  ax-5 674  ax-6 675  ax-gen 677  ax-8 798  ax-9 799  ax-12 802

This theorem depends on definitions:  df-bi 128  df-an 198  df-ex 679

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