Theorem equsb2 1760

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 1741	. 2 |- ( A. x ( x = y -> y = x ) -> [ y / x ] y = x )
2		equcomi 1681	. 2 |- ( x = y -> y = x )
3	1, 2	mpg 1428	1 |- [ y / x ] y = x

Syntax hints:   -> wi 4   [wsb 1736

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 1424  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515

This theorem depends on definitions:  df-bi 116  df-sb 1737

This theorem is referenced by:  sbco  1942