Theorem eqt2b 818

Description: An equivalence law for equality.

Assertion

Ref	Expression
eqt2b	|- (x = y -> (z = x <-> z = y))

Proof of Theorem eqt2b

Step	Hyp	Ref	Expression
1		eqt2 815	. 2 |- (x = y -> (z = x -> z = y))
2		eqt2 815	. . 3 |- (y = x -> (z = y -> z = x))
3	2	eqcoms 813	. 2 |- (x = y -> (z = y -> z = x))
4	1, 3	impbid 397	1 |- (x = y -> (z = x <-> z = y))

Syntax hints:   -> wi 2   <-> wb 127   = weq 797

This theorem is referenced by:  ddeeq2 1002  euf 1011  mo 1020  axac 1085  zfpair 1891  aceq0 3553  axpowndlem4 3746  zfcndac 3765

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

metamath.org