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Mirrors > Home > NFE Home > Th. List > moim | Unicode version |
Description: "At most one" is preserved through implication (notice wff reversal). (Contributed by NM, 22-Apr-1995.) |
Ref | Expression |
---|---|
moim |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | imim1 70 | . . . 4 | |
2 | 1 | al2imi 1561 | . . 3 |
3 | 2 | eximdv 1622 | . 2 |
4 | nfv 1619 | . . 3 | |
5 | 4 | mo2 2233 | . 2 |
6 | nfv 1619 | . . 3 | |
7 | 6 | mo2 2233 | . 2 |
8 | 3, 5, 7 | 3imtr4g 261 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wal 1540 wex 1541 wceq 1642 wmo 2205 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1546 ax-5 1557 ax-17 1616 ax-9 1654 ax-8 1675 ax-6 1729 ax-7 1734 ax-11 1746 ax-12 1925 |
This theorem depends on definitions: df-bi 177 df-or 359 df-an 360 df-tru 1319 df-ex 1542 df-nf 1545 df-sb 1649 df-eu 2208 df-mo 2209 |
This theorem is referenced by: moimi 2251 euimmo 2253 moexex 2273 rmoim 3035 rmoimi2 3037 funmo 5125 |
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