Theorem neeq2i 2528

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 2526	. 2 |- (A = B -> (C =/= A <-> C =/= B))
3	1, 2	ax-mp 5	1 |- (C =/= A <-> C =/= B)

Syntax hints:   <-> wb 176   = wceq 1642   =/= wne 2517

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-11 1746  ax-ext 2334

This theorem depends on definitions:  df-bi 177  df-ex 1542  df-cleq 2346  df-ne 2519

This theorem is referenced by:  neeq12i  2529  neeqtri  2538  nulnnn  4557  nchoicelem14  6303  nchoicelem17  6306