Theorem equtr 1129

Description: A transitive law for equality.

Assertion

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

Proof of Theorem equtr

Step	Hyp	Ref	Expression
1		ax-8 962	. 2 ⊢ (y = x → (y = z → x = z))
2	1	equcoms 1128	1 ⊢ (x = y → (y = z → x = z))

Syntax hints:   → wi 3   = wceq 954

This theorem is referenced by:  equtrr 1130  equtr2 1131  equequ1 1132  equvin 1273  a12lem1 1374  axsep 2697  dscmet 7870

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-gen 961  ax-8 962  ax-12 966  ax-4 971  ax-5o 973  ax-6o 976  ax-9o 1121

Copyright terms: Public domain