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Theorem nfmo 2578
Description: Bound-variable hypothesis builder for the at-most-one quantifier. Note that 𝑥 and 𝑦 need not be disjoint. (Contributed by NM, 9-Mar-1995.)
Hypothesis
Ref Expression
nfmo.1 𝑥𝜑
Assertion
Ref Expression
nfmo 𝑥∃*𝑦𝜑

Proof of Theorem nfmo
StepHypRef Expression
1 nftru 1899 . . 3 𝑦
2 nfmo.1 . . . 4 𝑥𝜑
32a1i 11 . . 3 (⊤ → Ⅎ𝑥𝜑)
41, 3nfmod 2577 . 2 (⊤ → Ⅎ𝑥∃*𝑦𝜑)
54mptru 1660 1 𝑥∃*𝑦𝜑
Colors of variables: wff setvar class
Syntax hints:  wtru 1653  wnf 1878  ∃*wmo 2562
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1890  ax-4 1904  ax-5 2005  ax-6 2069  ax-7 2105  ax-10 2183  ax-11 2198  ax-12 2211  ax-13 2349
This theorem depends on definitions:  df-bi 198  df-an 385  df-or 874  df-tru 1656  df-ex 1875  df-nf 1879  df-mo 2564
This theorem is referenced by:  mo3  2627  moexex  2662  2moex  2664  2euex  2665  2mo  2672  reusv1  5031  reusv2lem1  5032  mosubopt  5130  dffun6f  6081
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