Theorem equtr 2019

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		ax7 2014	. 2 ⊢ (𝑦 = 𝑥 → (𝑦 = 𝑧 → 𝑥 = 𝑧))
2	1	equcoms 2018	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-3 8  ax-gen 1794  ax-4 1808  ax-5 1909  ax-6 1966  ax-7 2006

This theorem depends on definitions:  df-bi 207  df-an 396  df-ex 1779

This theorem is referenced by:  equtrr  2020  equequ1  2023  equvinva  2028  ax6e  2387  equvini  2459  axprlem3OLD  5427