Theorem equtr 2018

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 2013	. 2 ⊢ (𝑦 = 𝑥 → (𝑦 = 𝑧 → 𝑥 = 𝑧))
2	1	equcoms 2017	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 1792  ax-4 1806  ax-5 1908  ax-6 1965  ax-7 2005

This theorem depends on definitions:  df-bi 207  df-an 396  df-ex 1777

This theorem is referenced by:  equtrr  2019  equequ1  2022  equvinva  2027  ax6e  2386  equvini  2458  axprlem3OLD  5434