Theorem equtr 2027

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 2022	. 2 ⊢ (𝑦 = 𝑥 → (𝑦 = 𝑧 → 𝑥 = 𝑧))
2	1	equcoms 2026	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 1795  ax-4 1809  ax-5 1910  ax-6 1969  ax-7 2014

This theorem depends on definitions:  df-bi 209  df-an 399  df-ex 1780

This theorem is referenced by:  equtrr  2028  equequ1  2031  equvinva  2036  ax6e  2400  equvini  2476  equviniOLD  2477  sbequiOLD  2533  sbequiALT  2595  axprlem3  5329