Theorem equequ1 1638

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 1435	. 2 |- ( x = y -> ( x = z -> y = z ) )
2		equtr 1635	. 2 |- ( x = y -> ( y = z -> x = z ) )
3	1, 2	impbid 127	1 |- ( x = y -> ( x = z <-> y = z ) )

Syntax hints:   -> wi 4   <-> wb 103

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-gen 1378  ax-ie2 1423  ax-8 1435  ax-17 1459  ax-i9 1463

This theorem depends on definitions:  df-bi 115

This theorem is referenced by:  equveli  1682  drsb1  1720  equsb3lem  1865  euequ1  2036  axext3  2064  reu6  2781  reu7  2787  cbviota  4892  dff13f  5430  poxp  5873  supmoti  6406  isoti  6420