Theorem necon3bii 2383

Description: Inference from equality to inequality. (Contributed by NM, 23-Feb-2005.)

Hypothesis

Ref	Expression
necon3bii.1	|- ( A = B <-> C = D )

Assertion

Ref	Expression
necon3bii	|- ( A =/= B <-> C =/= D )

Proof of Theorem necon3bii

Step	Hyp	Ref	Expression
1		necon3bii.1	. . 3 |- ( A = B <-> C = D )
2	1	necon3abii 2381	. 2 |- ( A =/= B <-> -. C = D )
3		df-ne 2346	. 2 |- ( C =/= D <-> -. C = D )
4	2, 3	bitr4i 187	1 |- ( A =/= B <-> C =/= D )

Syntax hints:   -. wn 3   <-> wb 105   = wceq 1353   =/= wne 2345

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 614  ax-in2 615

This theorem depends on definitions:  df-bi 117  df-ne 2346

This theorem is referenced by:  necom  2429  negne0bi  8204