Theorem equsb1 1838

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 1820	. 2 |- ( A. x ( x = y -> x = y ) -> [ y / x ] x = y )
2		id 19	. 2 |- ( x = y -> x = y )
3	1, 2	mpg 1504	1 |- [ y / x ] x = y

Syntax hints:   -> wi 4   [wsb 1815

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 1500  ax-gen 1502  ax-ie1 1546  ax-ie2 1547  ax-4 1563  ax-i9 1583  ax-ial 1587

This theorem depends on definitions:  df-bi 117  df-sb 1816

This theorem is referenced by:  sbcocom  2030  elsb1  2216  elsb2  2217  pm13.183  2964  exss  4362  relelfvdm  5722