Theorem eqtr3OLD 2764

Description: Obsolete version of eqtr3 2763 as of 24-Oct-2024. (Contributed by NM, 20-May-2005.) (New usage is discouraged.) (Proof modification is discouraged.)

Assertion

Ref	Expression
eqtr3OLD	⊢ ((𝐴 = 𝐶 ∧ 𝐵 = 𝐶) → 𝐴 = 𝐵)

Proof of Theorem eqtr3OLD

Step	Hyp	Ref	Expression
1		eqcom 2744	. 2 ⊢ (𝐵 = 𝐶 ↔ 𝐶 = 𝐵)
2		eqtr 2760	. 2 ⊢ ((𝐴 = 𝐶 ∧ 𝐶 = 𝐵) → 𝐴 = 𝐵)
3	1, 2	sylan2b 597	1 ⊢ ((𝐴 = 𝐶 ∧ 𝐵 = 𝐶) → 𝐴 = 𝐵)

Syntax hints:   → wi 4   ∧ wa 399   = wceq 1543

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1803  ax-4 1817  ax-5 1918  ax-6 1976  ax-7 2016  ax-9 2120  ax-ext 2708

This theorem depends on definitions:  df-bi 210  df-an 400  df-ex 1788  df-cleq 2729

This theorem is referenced by: (None)