Theorem neeq2i 1591

Description: Inference for inequality.

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 1589	. 2 |- (A = B -> (C =/= A <-> C =/= B))
3	1, 2	ax-mp 7	1 |- (C =/= A <-> C =/= B)

Syntax hints:   <-> wb 146   = wceq 955   =/= wne 1583

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-gen 962  ax-17 970  ax-4 972  ax-5o 974  ax-ext 1458

This theorem depends on definitions:  df-bi 147  df-an 225  df-cleq 1468  df-ne 1585

Copyright terms: Public domain