Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > neeqtrri | GIF version |
Description: Substitution of equal classes into an inequality. (Contributed by NM, 4-Jul-2012.) |
Ref | Expression |
---|---|
neeqtrr.1 | ⊢ 𝐴 ≠ 𝐵 |
neeqtrr.2 | ⊢ 𝐶 = 𝐵 |
Ref | Expression |
---|---|
neeqtrri | ⊢ 𝐴 ≠ 𝐶 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | neeqtrr.1 | . 2 ⊢ 𝐴 ≠ 𝐵 | |
2 | neeqtrr.2 | . . 3 ⊢ 𝐶 = 𝐵 | |
3 | 2 | eqcomi 2141 | . 2 ⊢ 𝐵 = 𝐶 |
4 | 1, 3 | neeqtri 2333 | 1 ⊢ 𝐴 ≠ 𝐶 |
Colors of variables: wff set class |
Syntax hints: = wceq 1331 ≠ wne 2306 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-in1 603 ax-in2 604 ax-5 1423 ax-gen 1425 ax-4 1487 ax-17 1506 ax-ext 2119 |
This theorem depends on definitions: df-bi 116 df-cleq 2130 df-ne 2307 |
This theorem is referenced by: pnfnemnf 7813 basendxnplusgndx 12054 plusgndxnmulrndx 12061 basendxnmulrndx 12062 |
Copyright terms: Public domain | W3C validator |