Theorem equsb1 1773

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 1755	. 2 ⊢ (∀𝑥(𝑥 = 𝑦 → 𝑥 = 𝑦) → [𝑦 / 𝑥]𝑥 = 𝑦)
2		id 19	. 2 ⊢ (𝑥 = 𝑦 → 𝑥 = 𝑦)
3	1, 2	mpg 1439	1 ⊢ [𝑦 / 𝑥]𝑥 = 𝑦

Syntax hints:   → wi 4  [wsb 1750

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1435  ax-gen 1437  ax-ie1 1481  ax-ie2 1482  ax-4 1498  ax-i9 1518  ax-ial 1522

This theorem depends on definitions:  df-bi 116  df-sb 1751

This theorem is referenced by:  sbcocom  1958  elsb1  2143  elsb2  2144  pm13.183  2864  exss  4205  relelfvdm  5518