Theorem equsb1v 2306

Description: Version of equsb1 2500 with a disjoint variable condition, which does not require ax-13 2391. (Contributed by BJ, 11-Sep-2019.)

Assertion

Ref	Expression
equsb1v	⊢ [𝑦 / 𝑥]𝑥 = 𝑦

Distinct variable group:   𝑥,𝑦

Proof of Theorem equsb1v

Step	Hyp	Ref	Expression
1		sb2v 2302	. 2 ⊢ (∀𝑥(𝑥 = 𝑦 → 𝑥 = 𝑦) → [𝑦 / 𝑥]𝑥 = 𝑦)
2		id 22	. 2 ⊢ (𝑥 = 𝑦 → 𝑥 = 𝑦)
3	1, 2	mpg 1898	1 ⊢ [𝑦 / 𝑥]𝑥 = 𝑦

Syntax hints:   → wi 4  [wsb 2069

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1896  ax-4 1910  ax-5 2011  ax-6 2077  ax-7 2114  ax-12 2222

This theorem depends on definitions:  df-bi 199  df-an 387  df-ex 1881  df-sb 2070

This theorem is referenced by:  sbiev  2345