Theorem equequ1 1646

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 1441	. 2 |- ( x = y -> ( x = z -> y = z ) )
2		equtr 1643	. 2 |- ( x = y -> ( y = z -> x = z ) )
3	1, 2	impbid 128	1 |- ( x = y -> ( x = z <-> y = z ) )

Syntax hints:   -> wi 4   <-> wb 104

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-gen 1384  ax-ie2 1429  ax-8 1441  ax-17 1465  ax-i9 1469

This theorem depends on definitions:  df-bi 116

This theorem is referenced by:  equveli  1690  drsb1  1728  equsb3lem  1873  euequ1  2044  axext3  2072  reu6  2807  reu7  2813  disjiun  3848  cbviota  5000  dff13f  5565  poxp  6013  dcdifsnid  6279  supmoti  6744  isoti  6758  fsum2dlemstep  10891