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Theorem nfmo 2562
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.)
Hypothesis
Ref Expression
nfmo.1 𝑥𝜑
Assertion
Ref Expression
nfmo 𝑥∃*𝑦𝜑

Proof of Theorem nfmo
StepHypRef Expression
1 nftru 1804 . . 3 𝑦
2 nfmo.1 . . . 4 𝑥𝜑
32a1i 11 . . 3 (⊤ → Ⅎ𝑥𝜑)
41, 3nfmod 2561 . 2 (⊤ → Ⅎ𝑥∃*𝑦𝜑)
54mptru 1547 1 𝑥∃*𝑦𝜑
Colors of variables: wff setvar class
Syntax hints:  wtru 1541  wnf 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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