Theorem equtrr 1724

Description: A transitive law for equality. Lemma L17 in [Megill] p. 446 (p. 14 of the preprint). (Contributed by NM, 23-Aug-1993.)

Assertion

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

Proof of Theorem equtrr

Step	Hyp	Ref	Expression
1		equtr 1723	. 2 |- ( z = x -> ( x = y -> z = y ) )
2	1	com12 30	1 |- ( x = y -> ( z = x -> z = y ) )

Syntax hints:   -> wi 4

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-gen 1463  ax-ie2 1508  ax-8 1518  ax-17 1540  ax-i9 1544

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  equtr2  1725  equequ2  1727