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| Description: Bound-variable hypothesis builder for the at-most-one quantifier. Note that 𝑥 and 𝑦 need not be disjoint. Usage of this theorem is discouraged because it depends on ax-13 2377. Use the weaker nfmov 2560 when possible. (Contributed by NM, 9-Mar-1995.) (New usage is discouraged.) | 
| Ref | Expression | 
|---|---|
| nfmo.1 | ⊢ Ⅎ𝑥𝜑 | 
| Ref | Expression | 
|---|---|
| nfmo | ⊢ Ⅎ𝑥∃*𝑦𝜑 | 
| Step | Hyp | Ref | Expression | 
|---|---|---|---|
| 1 | nftru 1804 | . . 3 ⊢ Ⅎ𝑦⊤ | |
| 2 | nfmo.1 | . . . 4 ⊢ Ⅎ𝑥𝜑 | |
| 3 | 2 | a1i 11 | . . 3 ⊢ (⊤ → Ⅎ𝑥𝜑) | 
| 4 | 1, 3 | nfmod 2561 | . 2 ⊢ (⊤ → Ⅎ𝑥∃*𝑦𝜑) | 
| 5 | 4 | mptru 1547 | 1 ⊢ Ⅎ𝑥∃*𝑦𝜑 | 
| Colors of variables: wff setvar class | 
| Syntax hints: ⊤wtru 1541 Ⅎwnf 1783 ∃*wmo 2538 | 
| This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1795 ax-4 1809 ax-5 1910 ax-6 1967 ax-7 2007 ax-10 2141 ax-11 2157 ax-12 2177 ax-13 2377 | 
| This theorem depends on definitions: df-bi 207 df-an 396 df-or 849 df-tru 1543 df-ex 1780 df-nf 1784 df-mo 2540 | 
| This theorem is referenced by: moexex 2638 2moex 2640 2euex 2641 | 
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