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Mirrors > Home > ILE Home > Th. List > moanimv | GIF version |
Description: Introduction of a conjunct into at-most-one quantifier. (Contributed by NM, 23-Mar-1995.) |
Ref | Expression |
---|---|
moanimv | ⊢ (∃*𝑥(𝜑 ∧ 𝜓) ↔ (𝜑 → ∃*𝑥𝜓)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfv 1491 | . 2 ⊢ Ⅎ𝑥𝜑 | |
2 | 1 | moanim 2049 | 1 ⊢ (∃*𝑥(𝜑 ∧ 𝜓) ↔ (𝜑 → ∃*𝑥𝜓)) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∧ wa 103 ↔ wb 104 ∃*wmo 1976 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 681 ax-5 1406 ax-7 1407 ax-gen 1408 ax-ie1 1452 ax-ie2 1453 ax-8 1465 ax-10 1466 ax-11 1467 ax-i12 1468 ax-bndl 1469 ax-4 1470 ax-17 1489 ax-i9 1493 ax-ial 1497 ax-i5r 1498 |
This theorem depends on definitions: df-bi 116 df-nf 1420 df-sb 1719 df-eu 1978 df-mo 1979 |
This theorem is referenced by: mosubt 2830 2reuswapdc 2857 2rmorex 2859 mosubopt 4564 funmo 5096 funcnv 5142 fncnv 5147 isarep2 5168 fnres 5197 fnopabg 5204 fvopab3ig 5449 opabex 5598 fnoprabg 5826 ovidi 5843 ovig 5846 oprabexd 5979 oprabex 5980 th3qcor 6487 dvfgg 12612 |
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