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))

Syntax hints:   → wi 4

This theorem was proved from 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 theorem depends on definitions:  df-bi 177  df-ex 1542

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