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Theorem nfmo 2644
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 1798 . . 3 𝑦
2 nfmo.1 . . . 4 𝑥𝜑
32a1i 11 . . 3 (⊤ → Ⅎ𝑥𝜑)
41, 3nfmod 2643 . 2 (⊤ → Ⅎ𝑥∃*𝑦𝜑)
54mptru 1537 1 𝑥∃*𝑦𝜑
Colors of variables: wff setvar class
Syntax hints:  wtru 1531  wnf 1777  ∃*wmo 2618
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1904  ax-6 1963  ax-7 2008  ax-10 2138  ax-11 2153  ax-12 2169  ax-13 2385
This theorem depends on definitions:  df-bi 208  df-an 397  df-or 844  df-tru 1533  df-ex 1774  df-nf 1778  df-mo 2620
This theorem is referenced by:  moexex  2722  2moex  2724  2euex  2725
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