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Theorem nfmod 2605
Description: Bound-variable hypothesis builder for the at-most-one quantifier. Deduction version of nfmo 2606. (Contributed by Mario Carneiro, 14-Nov-2016.)
Hypotheses
Ref Expression
nfmod.1 𝑦𝜑
nfmod.2 (𝜑 → Ⅎ𝑥𝜓)
Assertion
Ref Expression
nfmod (𝜑 → Ⅎ𝑥∃*𝑦𝜓)

Proof of Theorem nfmod
StepHypRef Expression
1 nfmod.1 . 2 𝑦𝜑
2 nfmod.2 . . 3 (𝜑 → Ⅎ𝑥𝜓)
32adantr 473 . 2 ((𝜑 ∧ ¬ ∀𝑥 𝑥 = 𝑦) → Ⅎ𝑥𝜓)
41, 3nfmod2 2603 1 (𝜑 → Ⅎ𝑥∃*𝑦𝜓)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wal 1651  wnf 1879  ∃*wmo 2589
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1891  ax-4 1905  ax-5 2006  ax-6 2072  ax-7 2107  ax-10 2185  ax-11 2200  ax-12 2213  ax-13 2377
This theorem depends on definitions:  df-bi 199  df-an 386  df-or 875  df-tru 1657  df-ex 1876  df-nf 1880  df-mo 2591
This theorem is referenced by:  nfmo  2606  wl-mo3t  33848
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