Theorem neirr 2522

Description: No class is unequal to itself. (Contributed by Stefan O'Rear, 1-Jan-2015.)

Assertion

Ref	Expression
neirr	⊢ ¬ A ≠ A

Proof of Theorem neirr

Step	Hyp	Ref	Expression
1		eqid 2353	. 2 ⊢ A = A
2		nne 2521	. 2 ⊢ (¬ A ≠ A ↔ A = A)
3	1, 2	mpbir 200	1 ⊢ ¬ A ≠ A

Syntax hints:  ¬ wn 3   = 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-ext 2334

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

This theorem is referenced by:  neldifsn  3842  ltcirr  6273