Theorem equequ1 1598

Description: An equivalence law for equality. (Contributed by NM, 5-Aug-1993.)

Assertion

Ref	Expression
equequ1	|- ( x = y -> ( x = z <-> y = z ) )

Proof of Theorem equequ1

Step	Hyp	Ref	Expression
1		ax-8 1395	. 2 |- ( x = y -> ( x = z -> y = z ) )
2		equtr 1595	. 2 |- ( x = y -> ( y = z -> x = z ) )
3	1, 2	impbid 120	1 |- ( x = y -> ( x = z <-> y = z ) )

Syntax hints:   -> wi 4   <-> wb 98

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-gen 1338  ax-ie2 1383  ax-8 1395  ax-17 1419  ax-i9 1423

This theorem depends on definitions:  df-bi 110

This theorem is referenced by:  equveli  1642  drsb1  1680  equsb3lem  1824  euequ1  1995  axext3  2023  reu6  2730  reu7  2736  cbviota  4872  dff13f  5409  poxp  5853