Theorem equequ1 1712

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 1504	. 2 |- ( x = y -> ( x = z -> y = z ) )
2		equtr 1709	. 2 |- ( x = y -> ( y = z -> x = z ) )
3	1, 2	impbid 129	1 |- ( x = y -> ( x = z <-> y = z ) )

Syntax hints:   -> wi 4   <-> wb 105

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-gen 1449  ax-ie2 1494  ax-8 1504  ax-17 1526  ax-i9 1530

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  equveli  1759  drsb1  1799  equsb3lem  1950  euequ1  2121  axext3  2160  cbvreuvw  2710  reu6  2927  reu7  2933  disjiun  3999  cbviota  5184  dff13f  5771  poxp  6233  dcdifsnid  6505  supmoti  6992  isoti  7006  nninfwlpoim  7176  exmidontriimlem3  7222  exmidontriim  7224  netap  7253  fsum2dlemstep  11442  ennnfonelemr  12424  ctinf  12431  reap0  14809