Theorem equsb2 1784

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 1765	. 2 |- ( A. x ( x = y -> y = x ) -> [ y / x ] y = x )
2		equcomi 1702	. 2 |- ( x = y -> y = x )
3	1, 2	mpg 1449	1 |- [ y / x ] y = x

Syntax hints:   -> wi 4   [wsb 1760

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 1445  ax-gen 1447  ax-ie1 1491  ax-ie2 1492  ax-8 1502  ax-4 1508  ax-17 1524  ax-i9 1528  ax-ial 1532

This theorem depends on definitions:  df-bi 117  df-sb 1761

This theorem is referenced by:  sbco  1966