Theorem equtr 1731

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 1526	. 2 ⊢ (𝑦 = 𝑥 → (𝑦 = 𝑧 → 𝑥 = 𝑧))
2	1	equcoms 1730	1 ⊢ (𝑥 = 𝑦 → (𝑦 = 𝑧 → 𝑥 = 𝑧))

Syntax hints:   → wi 4

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-gen 1471  ax-ie2 1516  ax-8 1526  ax-17 1548  ax-i9 1552

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  equtrr  1732  equequ1  1734  equveli  1781  equvin  1885