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Mirrors > Home > NFE 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 1619 | . 2 ⊢ Ⅎxφ | |
2 | 1 | moanim 2260 | 1 ⊢ (∃*x(φ ∧ ψ) ↔ (φ → ∃*xψ)) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ↔ wb 176 ∧ wa 358 ∃*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: 2reuswap 3038 2reu5lem2 3042 funmo 5125 funsn 5147 funcnv 5156 fncnv 5158 fnres 5199 fnopabg 5205 fvopab3ig 5387 fnoprabg 5585 ovidi 5594 ovig 5597 |
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