Theorem equsb1 2034

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 2023	. 2 ⊢ (∀x(x = y → x = y) → [y / x]x = y)
2		id 19	. 2 ⊢ (x = y → x = y)
3	1, 2	mpg 1548	1 ⊢ [y / x]x = y

Syntax hints:   → wi 4  [wsb 1648

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925

This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649

This theorem is referenced by:  sbequ8  2079  pm13.183  2980