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Mirrors > Home > ILE Home > Th. List > moimi | GIF version |
Description: "At most one" is preserved through implication (notice wff reversal). (Contributed by NM, 15-Feb-2006.) |
Ref | Expression |
---|---|
moimi.1 | ⊢ (𝜑 → 𝜓) |
Ref | Expression |
---|---|
moimi | ⊢ (∃*𝑥𝜓 → ∃*𝑥𝜑) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | moim 2077 | . 2 ⊢ (∀𝑥(𝜑 → 𝜓) → (∃*𝑥𝜓 → ∃*𝑥𝜑)) | |
2 | moimi.1 | . 2 ⊢ (𝜑 → 𝜓) | |
3 | 1, 2 | mpg 1438 | 1 ⊢ (∃*𝑥𝜓 → ∃*𝑥𝜑) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∃*wmo 2014 |
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-io 699 ax-5 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-10 1492 ax-11 1493 ax-i12 1494 ax-bndl 1496 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 |
This theorem depends on definitions: df-bi 116 df-nf 1448 df-sb 1750 df-eu 2016 df-mo 2017 |
This theorem is referenced by: moan 2082 moor 2084 mooran1 2085 mooran2 2086 2moex 2099 2euex 2100 2exeu 2105 mosubt 2898 sndisj 3972 disjxsn 3974 mosubopt 4663 funcnvsn 5227 nfunsn 5514 th3qlem2 6595 shftfn 10752 |
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