Theorem equequ2OLD 1955

Description: Obsolete proof of equequ2 1953 as of 12-Apr-2021. (Contributed by NM, 21-Jun-1993.) (Proof shortened by Wolf Lammen, 4-Aug-2017.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

Ref	Expression
equequ2OLD	⊢ (𝑥 = 𝑦 → (𝑧 = 𝑥 ↔ 𝑧 = 𝑦))

Proof of Theorem equequ2OLD

Step	Hyp	Ref	Expression
1		equequ1 1952	. 2 ⊢ (𝑥 = 𝑦 → (𝑥 = 𝑧 ↔ 𝑦 = 𝑧))
2		equcom 1945	. 2 ⊢ (𝑥 = 𝑧 ↔ 𝑧 = 𝑥)
3		equcom 1945	. 2 ⊢ (𝑦 = 𝑧 ↔ 𝑧 = 𝑦)
4	1, 2, 3	3bitr3g 302	1 ⊢ (𝑥 = 𝑦 → (𝑧 = 𝑥 ↔ 𝑧 = 𝑦))

Syntax hints:   → wi 4   ↔ wb 196

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935

This theorem depends on definitions:  df-bi 197  df-an 386  df-ex 1705

This theorem is referenced by: (None)