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Mirrors > Home > ILE Home > Th. List > nonconne | Unicode version |
Description: Law of noncontradiction with equality and inequality. (Contributed by NM, 3-Feb-2012.) |
Ref | Expression |
---|---|
nonconne |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pm3.24 683 | . 2 | |
2 | df-ne 2335 | . . 3 | |
3 | 2 | anbi2i 453 | . 2 |
4 | 1, 3 | mtbir 661 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wa 103 wceq 1342 wne 2334 |
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 604 ax-in2 605 |
This theorem depends on definitions: df-bi 116 df-ne 2335 |
This theorem is referenced by: (None) |
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