Theorem bj-equsb1v 32762

Description: Version of equsb1 2368 with a dv condition, which does not require ax-13 2246. (Contributed by BJ, 11-Sep-2019.) (Proof modification is discouraged.)

Assertion

Ref	Expression
bj-equsb1v	⊢ [𝑦 / 𝑥]𝑥 = 𝑦

Distinct variable group:   𝑥,𝑦

Proof of Theorem bj-equsb1v

Step	Hyp	Ref	Expression
1		bj-sb2v 32753	. 2 ⊢ (∀𝑥(𝑥 = 𝑦 → 𝑥 = 𝑦) → [𝑦 / 𝑥]𝑥 = 𝑦)
2		id 22	. 2 ⊢ (𝑥 = 𝑦 → 𝑥 = 𝑦)
3	1, 2	mpg 1724	1 ⊢ [𝑦 / 𝑥]𝑥 = 𝑦

Syntax hints:   → wi 4  [wsb 1880

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  ax-12 2047

This theorem depends on definitions:  df-bi 197  df-an 386  df-ex 1705  df-sb 1881

This theorem is referenced by: (None)