Theorem equsb2 1809

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 1790	. 2 |- ( A. x ( x = y -> y = x ) -> [ y / x ] y = x )
2		equcomi 1727	. 2 |- ( x = y -> y = x )
3	1, 2	mpg 1474	1 |- [ y / x ] y = x

Syntax hints:   -> wi 4   [wsb 1785

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 1470  ax-gen 1472  ax-ie1 1516  ax-ie2 1517  ax-8 1527  ax-4 1533  ax-17 1549  ax-i9 1553  ax-ial 1557

This theorem depends on definitions:  df-bi 117  df-sb 1786

This theorem is referenced by:  sbco  1996