Theorem equsb2 2510

Description: Substitution applied to an atomic wff. Usage of this theorem is discouraged because it depends on ax-13 2379. Check out equsb1v 2109 for a version requiring less axioms. (Contributed by NM, 10-May-1993.) (New usage is discouraged.)

Assertion

Ref	Expression
equsb2	⊢ [𝑦 / 𝑥]𝑦 = 𝑥

Proof of Theorem equsb2

Step	Hyp	Ref	Expression
1		sb2 2493	. 2 ⊢ (∀𝑥(𝑥 = 𝑦 → 𝑦 = 𝑥) → [𝑦 / 𝑥]𝑦 = 𝑥)
2		equcomi 2024	. 2 ⊢ (𝑥 = 𝑦 → 𝑦 = 𝑥)
3	1, 2	mpg 1799	1 ⊢ [𝑦 / 𝑥]𝑦 = 𝑥

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 1797  ax-4 1811  ax-5 1911  ax-6 1970  ax-7 2015  ax-10 2142  ax-12 2175  ax-13 2379

This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-ex 1782  df-nf 1786  df-sb 2070

This theorem is referenced by:  bj-sbidmOLD  34604