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Mirrors > Home > ILE Home > Th. List > necon4addc | Unicode version |
Description: Contrapositive inference for inequality. (Contributed by Jim Kingdon, 17-May-2018.) |
Ref | Expression |
---|---|
necon4addc.1 | DECID |
Ref | Expression |
---|---|
necon4addc | DECID |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | necon4addc.1 | . 2 DECID | |
2 | df-ne 2307 | . . . 4 | |
3 | 2 | imbi1i 237 | . . 3 |
4 | condc 838 | . . 3 DECID | |
5 | 3, 4 | syl5bi 151 | . 2 DECID |
6 | 1, 5 | sylcom 28 | 1 DECID |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 DECID wdc 819 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-io 698 |
This theorem depends on definitions: df-bi 116 df-stab 816 df-dc 820 df-ne 2307 |
This theorem is referenced by: (None) |
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