Theorem equsb1 1708

Description: Substitution applied to an atomic wff. (Contributed by NM, 5-Aug-1993.)

Assertion

Ref	Expression
equsb1	⊢ [𝑦 / 𝑥]𝑥 = 𝑦

Proof of Theorem equsb1

Step	Hyp	Ref	Expression
1		sb2 1690	. 2 ⊢ (∀𝑥(𝑥 = 𝑦 → 𝑥 = 𝑦) → [𝑦 / 𝑥]𝑥 = 𝑦)
2		id 19	. 2 ⊢ (𝑥 = 𝑦 → 𝑥 = 𝑦)
3	1, 2	mpg 1380	1 ⊢ [𝑦 / 𝑥]𝑥 = 𝑦

Syntax hints:   → wi 4  [wsb 1685

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1376  ax-gen 1378  ax-ie1 1422  ax-ie2 1423  ax-4 1440  ax-i9 1463  ax-ial 1467

This theorem depends on definitions:  df-bi 115  df-sb 1686

This theorem is referenced by:  sbcocom  1885  elsb3  1893  elsb4  1894  pm13.183  2732  exss  3982  relelfvdm  5226