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Mirrors > Home > MPE Home > Th. List > nfmo | Structured version Visualization version GIF version |
Description: Bound-variable hypothesis builder for "at most one." (Contributed by NM, 9-Mar-1995.) |
Ref | Expression |
---|---|
nfeu.1 | ⊢ Ⅎ𝑥𝜑 |
Ref | Expression |
---|---|
nfmo | ⊢ Ⅎ𝑥∃*𝑦𝜑 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nftru 1730 | . . 3 ⊢ Ⅎ𝑦⊤ | |
2 | nfeu.1 | . . . 4 ⊢ Ⅎ𝑥𝜑 | |
3 | 2 | a1i 11 | . . 3 ⊢ (⊤ → Ⅎ𝑥𝜑) |
4 | 1, 3 | nfmod 2485 | . 2 ⊢ (⊤ → Ⅎ𝑥∃*𝑦𝜑) |
5 | 4 | trud 1493 | 1 ⊢ Ⅎ𝑥∃*𝑦𝜑 |
Colors of variables: wff setvar class |
Syntax hints: ⊤wtru 1484 Ⅎwnf 1708 ∃*wmo 2471 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-tru 1486 df-ex 1705 df-nf 1710 df-eu 2474 df-mo 2475 |
This theorem is referenced by: mo3 2507 moexex 2541 2moex 2543 2euex 2544 2mo 2551 reusv1 4866 reusv1OLD 4867 reusv2lem1 4868 mosubopt 4972 dffun6f 5902 |
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