Theorem equsb2 2524

Description: Substitution applied to an atomic wff. Usage of this theorem is discouraged because it depends on ax-13 2404. Check out equsb1v 2140 for a version requiring fewer 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 2511	. 2 ⊢ (∀𝑥(𝑥 = 𝑦 → 𝑦 = 𝑥) → [𝑦 / 𝑥]𝑦 = 𝑥)
2		equcomi 2047	. 2 ⊢ (𝑥 = 𝑦 → 𝑦 = 𝑥)
3	1, 2	mpg 1827	1 ⊢ [𝑦 / 𝑥]𝑦 = 𝑥

Syntax hints:   → wi 4  [wsb 2096

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1825  ax-4 1839  ax-5 1940  ax-6 1997  ax-7 2038  ax-10 2176  ax-12 2213  ax-13 2404

This theorem depends on definitions:  df-bi 210  df-an 401  df-or 861  df-ex 1810  df-nf 1814  df-sb 2097

This theorem is referenced by:  bj-sbidmOLD  37466