Theorem equsb2 2497

Description: Substitution applied to an atomic wff. Usage of this theorem is discouraged because it depends on ax-13 2373. Check out equsb1v 2106 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 2481	. 2 ⊢ (∀𝑥(𝑥 = 𝑦 → 𝑦 = 𝑥) → [𝑦 / 𝑥]𝑦 = 𝑥)
2		equcomi 2023	. 2 ⊢ (𝑥 = 𝑦 → 𝑦 = 𝑥)
3	1, 2	mpg 1803	1 ⊢ [𝑦 / 𝑥]𝑦 = 𝑥

Syntax hints:   → wi 4  [wsb 2070

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1801  ax-4 1815  ax-5 1916  ax-6 1974  ax-7 2014  ax-10 2140  ax-12 2174  ax-13 2373

This theorem depends on definitions:  df-bi 206  df-an 396  df-or 844  df-ex 1786  df-nf 1790  df-sb 2071

This theorem is referenced by:  bj-sbidmOLD  35013