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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 1964 | . 2 ⊢ (∀𝑥(𝜑 → 𝜓) → (∃*𝑥𝜓 → ∃*𝑥𝜑)) | |
2 | moimi.1 | . 2 ⊢ (𝜑 → 𝜓) | |
3 | 1, 2 | mpg 1340 | 1 ⊢ (∃*𝑥𝜓 → ∃*𝑥𝜑) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∃*wmo 1901 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 ax-4 1400 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 |
This theorem depends on definitions: df-bi 110 df-nf 1350 df-sb 1646 df-eu 1903 df-mo 1904 |
This theorem is referenced by: moan 1969 moor 1971 mooran1 1972 mooran2 1973 2moex 1986 2euex 1987 2exeu 1992 mosubt 2718 sndisj 3760 disjxsn 3762 mosubopt 4405 funcnvsn 4945 nfunsn 5207 th3qlem2 6209 shftfn 9425 |
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