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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 1528 | . 2 ⊢ Ⅎ𝑥𝜑 | |
2 | 1 | moanim 2100 | 1 ⊢ (∃*𝑥(𝜑 ∧ 𝜓) ↔ (𝜑 → ∃*𝑥𝜓)) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∧ wa 104 ↔ wb 105 ∃*wmo 2027 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-io 709 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 |
This theorem depends on definitions: df-bi 117 df-nf 1461 df-sb 1763 df-eu 2029 df-mo 2030 |
This theorem is referenced by: mosubt 2916 2reuswapdc 2943 2rmorex 2945 mosubopt 4693 funmo 5233 funcnv 5279 fncnv 5284 isarep2 5305 fnres 5334 fnopabg 5341 fvopab3ig 5592 opabex 5742 fnoprabg 5978 ovidi 5995 ovig 5998 oprabexd 6130 oprabex 6131 th3qcor 6641 dvfgg 14242 |
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