Theorem equtr 1682

Description: A transitive law for equality. (Contributed by NM, 23-Aug-1993.)

Assertion

Ref	Expression
equtr	⊢ (x = y → (y = z → x = z))

Proof of Theorem equtr

Step	Hyp	Ref	Expression
1		ax-8 1675	. 2 ⊢ (y = x → (y = z → x = z))
2	1	equcoms 1681	1 ⊢ (x = y → (y = z → x = z))

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:  equtrr  1683  equequ1  1684  equveli  1988  equvin  2001