Theorem neeq2i 2383

Description: Inference for inequality. (Contributed by NM, 29-Apr-2005.)

Hypothesis

Ref	Expression
neeq1i.1	|- A = B

Assertion

Ref	Expression
neeq2i	|- ( C =/= A <-> C =/= B )

Proof of Theorem neeq2i

Step	Hyp	Ref	Expression
1		neeq1i.1	. 2 |- A = B
2		neeq2 2381	. 2 |- ( A = B -> ( C =/= A <-> C =/= B ) )
3	1, 2	ax-mp 5	1 |- ( C =/= A <-> C =/= B )

Syntax hints:   <-> wb 105   = wceq 1364   =/= wne 2367

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-in1 615  ax-in2 616  ax-5 1461  ax-gen 1463  ax-4 1524  ax-17 1540  ax-ext 2178

This theorem depends on definitions:  df-bi 117  df-cleq 2189  df-ne 2368

This theorem is referenced by:  neeq12i  2384  neeqtri  2394  exmidsbthrlem  15753