Theorem equtr 2056

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 2051	. 2 ⊢ (𝑦 = 𝑥 → (𝑦 = 𝑧 → 𝑥 = 𝑧))
2	1	equcoms 2055	1 ⊢ (𝑥 = 𝑦 → (𝑦 = 𝑧 → 𝑥 = 𝑧))

This proof depends on syntax axioms:   → wi 4

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1828  ax-4 1842  ax-5 1945  ax-6 2002  ax-7 2043

This proof depends on definitions:  df-bi 210  df-an 402  df-ex 1813

This theorem is used by:  equtrr  2057  equequ1  2060  equvinva  2065  ax6e  2415  equvini  2487