Theorem equsb2 1711

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 1692	. 2 |- ( A. x ( x = y -> y = x ) -> [ y / x ] y = x )
2		equcomi 1633	. 2 |- ( x = y -> y = x )
3	1, 2	mpg 1381	1 |- [ y / x ] y = x

Syntax hints:   -> wi 4   [wsb 1687

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 1377  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468

This theorem depends on definitions:  df-bi 115  df-sb 1688

This theorem is referenced by:  sbco  1885