Theorem equsb2 1834

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 1815	. 2 |- ( A. x ( x = y -> y = x ) -> [ y / x ] y = x )
2		equcomi 1752	. 2 |- ( x = y -> y = x )
3	1, 2	mpg 1499	1 |- [ y / x ] y = x

Syntax hints:   -> wi 4   [wsb 1810

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 1495  ax-gen 1497  ax-ie1 1541  ax-ie2 1542  ax-8 1552  ax-4 1558  ax-17 1574  ax-i9 1578  ax-ial 1582

This theorem depends on definitions:  df-bi 117  df-sb 1811

This theorem is referenced by:  sbco  2021