Theorem neeq2i 2221

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 2219	. 2 |- ( A = B -> ( C =/= A <-> C =/= B ) )
3	1, 2	ax-mp 7	1 |- ( C =/= A <-> C =/= B )

Syntax hints:   <-> wb 98   = wceq 1243   =/= wne 2204

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-in1 544  ax-in2 545  ax-5 1336  ax-gen 1338  ax-4 1400  ax-17 1419  ax-ext 2022

This theorem depends on definitions:  df-bi 110  df-cleq 2033  df-ne 2206

This theorem is referenced by:  neeq12i  2222  neeqtri  2232