Theorem equsb1 1722

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 1704	. 2 |- ( A. x ( x = y -> x = y ) -> [ y / x ] x = y )
2		id 19	. 2 |- ( x = y -> x = y )
3	1, 2	mpg 1392	1 |- [ y / x ] x = y

Syntax hints:   -> wi 4   [wsb 1699

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1388  ax-gen 1390  ax-ie1 1434  ax-ie2 1435  ax-4 1452  ax-i9 1475  ax-ial 1479

This theorem depends on definitions:  df-bi 116  df-sb 1700

This theorem is referenced by:  sbcocom  1899  elsb3  1907  elsb4  1908  pm13.183  2768  exss  4078  relelfvdm  5371