Theorem equsb3vOLD 2508

Description: Obsolete version of equsb3v 2290 as of 19-Jan-2023. (Contributed by Raph Levien and FL, 4-Dec-2005.) (Proof shortened by Andrew Salmon, 14-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

Ref	Expression
equsb3vOLD	⊢ ([𝑥 / 𝑦]𝑦 = 𝑧 ↔ 𝑥 = 𝑧)

Distinct variable groups:   𝑦,𝑧   𝑥,𝑦

Proof of Theorem equsb3vOLD

Step	Hyp	Ref	Expression
1		nfv 1957	. 2 ⊢ Ⅎ𝑦 𝑥 = 𝑧
2		equequ1 2071	. 2 ⊢ (𝑦 = 𝑥 → (𝑦 = 𝑧 ↔ 𝑥 = 𝑧))
3	1, 2	sbie 2483	1 ⊢ ([𝑥 / 𝑦]𝑦 = 𝑧 ↔ 𝑥 = 𝑧)

Syntax hints:   ↔ wb 198  [wsb 2011

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1839  ax-4 1853  ax-5 1953  ax-6 2021  ax-7 2054  ax-10 2134  ax-12 2162  ax-13 2333

This theorem depends on definitions:  df-bi 199  df-an 387  df-or 837  df-ex 1824  df-nf 1828  df-sb 2012

This theorem is referenced by: (None)