Theorem nonconne 2524

Description: Law of noncontradiction with equality and inequality. (Contributed by NM, 3-Feb-2012.)

Assertion

Ref	Expression
nonconne	|- -. (A = B /\ A =/= B)

Proof of Theorem nonconne

Step	Hyp	Ref	Expression
1		pm3.24 852	. 2 |- -. (A = B /\ -. A = B)
2		df-ne 2519	. . 3 |- (A =/= B <-> -. A = B)
3	2	anbi2i 675	. 2 |- ((A = B /\ A =/= B) <-> (A = B /\ -. A = B))
4	1, 3	mtbir 290	1 |- -. (A = B /\ A =/= B)

Syntax hints:  -. wn 3   /\ wa 358   = wceq 1642   =/= wne 2517

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 177  df-an 360  df-ne 2519

This theorem is referenced by: (None)