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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 1879 | . . 3 ⊢ Ⅎ𝑦⊤ | |
2 | nfeu.1 | . . . 4 ⊢ Ⅎ𝑥𝜑 | |
3 | 2 | a1i 11 | . . 3 ⊢ (⊤ → Ⅎ𝑥𝜑) |
4 | 1, 3 | nfmod 2622 | . 2 ⊢ (⊤ → Ⅎ𝑥∃*𝑦𝜑) |
5 | 4 | trud 1642 | 1 ⊢ Ⅎ𝑥∃*𝑦𝜑 |
Colors of variables: wff setvar class |
Syntax hints: ⊤wtru 1633 Ⅎwnf 1857 ∃*wmo 2608 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1871 ax-4 1886 ax-5 1988 ax-6 2054 ax-7 2090 ax-10 2168 ax-11 2183 ax-12 2196 ax-13 2391 |
This theorem depends on definitions: df-bi 197 df-or 384 df-an 385 df-tru 1635 df-ex 1854 df-nf 1859 df-eu 2611 df-mo 2612 |
This theorem is referenced by: mo3 2645 moexex 2679 2moex 2681 2euex 2682 2mo 2689 reusv1 5015 reusv1OLD 5016 reusv2lem1 5017 mosubopt 5120 dffun6f 6063 |
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