Theorem equsb2 2369

Description: Substitution applied to an atomic wff. (Contributed by NM, 10-May-1993.)

Assertion

Ref	Expression
equsb2	⊢ [𝑦 / 𝑥]𝑦 = 𝑥

Proof of Theorem equsb2

Step	Hyp	Ref	Expression
1		sb2 2352	. 2 ⊢ (∀𝑥(𝑥 = 𝑦 → 𝑦 = 𝑥) → [𝑦 / 𝑥]𝑦 = 𝑥)
2		equcomi 1944	. 2 ⊢ (𝑥 = 𝑦 → 𝑦 = 𝑥)
3	1, 2	mpg 1724	1 ⊢ [𝑦 / 𝑥]𝑦 = 𝑥

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  ax-13 2246

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

This theorem is referenced by:  bj-sbidmOLD  32831