Theorem sbeq2 901

Description: Substitution applied to atomic wff.

Assertion

Ref	Expression
sbeq2	|- [y / x]y = x

Proof of Theorem sbeq2

Step	Hyp	Ref	Expression
1		sb2 859	. 2 |- (A.x(x = y -> y = x) -> [y / x]y = x)
2		eqcom 811	. 2 |- (x = y -> y = x)
3	1, 2	mpg 684	1 |- [y / x]y = x

Syntax hints:   -> wi 2   = weq 797  [wsb 852

This theorem is referenced by:  sbco 910

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6  ax-4 673  ax-5 674  ax-6 675  ax-gen 677  ax-8 798  ax-9 799  ax-12 802

This theorem depends on definitions:  df-bi 128  df-an 198  df-ex 679  df-sb 853

metamath.org