Theorem eqt2 815

Description: A transitive law for equality. Lemma L17 in [Megill] p. 446 (p. 14 of the preprint).

Assertion

Ref	Expression
eqt2	|- (x = y -> (z = x -> z = y))

Proof of Theorem eqt2

Step	Hyp	Ref	Expression
1		eqt 814	. 2 |- (z = x -> (x = y -> z = y))
2	1	com12 13	1 |- (x = y -> (z = x -> z = y))

Syntax hints:   -> wi 2   = weq 797

This theorem is referenced by:  eqt2b 818

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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