Theorem equsb2 1810

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

Assertion

Ref	Expression
equsb2	⊢ [𝑦 / 𝑥]𝑦 = 𝑥

Proof of Theorem equsb2

Step	Hyp	Ref	Expression
1		sb2 1791	. 2 ⊢ (∀𝑥(𝑥 = 𝑦 → 𝑦 = 𝑥) → [𝑦 / 𝑥]𝑦 = 𝑥)
2		equcomi 1728	. 2 ⊢ (𝑥 = 𝑦 → 𝑦 = 𝑥)
3	1, 2	mpg 1475	1 ⊢ [𝑦 / 𝑥]𝑦 = 𝑥

Syntax hints:   → wi 4  [wsb 1786

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1471  ax-gen 1473  ax-ie1 1517  ax-ie2 1518  ax-8 1528  ax-4 1534  ax-17 1550  ax-i9 1554  ax-ial 1558

This theorem depends on definitions:  df-bi 117  df-sb 1787

This theorem is referenced by:  sbco  1997