Theorem neii 2247

Description: Inference associated with df-ne 2246. (Contributed by BJ, 7-Jul-2018.)

Hypothesis

Ref	Expression
neii.1	⊢ 𝐴 ≠ 𝐵

Assertion

Ref	Expression
neii	⊢ ¬ 𝐴 = 𝐵

Proof of Theorem neii

Step	Hyp	Ref	Expression
1		neii.1	. 2 ⊢ 𝐴 ≠ 𝐵
2		df-ne 2246	. 2 ⊢ (𝐴 ≠ 𝐵 ↔ ¬ 𝐴 = 𝐵)
3	1, 2	mpbi 143	1 ⊢ ¬ 𝐴 = 𝐵

Syntax hints:  ¬ wn 3   = wceq 1284   ≠ wne 2245

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104

This theorem depends on definitions:  df-bi 115  df-ne 2246

This theorem is referenced by:  2dom  6308  ine0  7498  inelr  7684  xrltnr  8855  pnfnlt  8862  xrlttri3  8872  nltpnft  8884  3lcm2e6woprm  10468  6lcm4e12  10469