Theorem equsb1 1778

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 1760	. 2 |- ( A. x ( x = y -> x = y ) -> [ y / x ] x = y )
2		id 19	. 2 |- ( x = y -> x = y )
3	1, 2	mpg 1444	1 |- [ y / x ] x = y

Syntax hints:   -> wi 4   [wsb 1755

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1440  ax-gen 1442  ax-ie1 1486  ax-ie2 1487  ax-4 1503  ax-i9 1523  ax-ial 1527

This theorem depends on definitions:  df-bi 116  df-sb 1756

This theorem is referenced by:  sbcocom  1963  elsb1  2148  elsb2  2149  pm13.183  2868  exss  4212  relelfvdm  5528