Theorem equtrr 1683

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 1682	. 2 |- (z = x -> (x = y -> z = y))
2	1	com12 27	1 |- (x = y -> (z = x -> z = y))

This proof depends on syntax axioms:   -> wi 4

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675

This proof depends on definitions:  df-bi 177  df-ex 1542

This theorem is used by:  equtr2  1688  ax12b  1689  ax12bOLD  1690  ax12  1935  ax12from12o  2156  ax11eq  2193