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Theorem mobidv 2042
 Description: Formula-building rule for "at most one" quantifier (deduction form). (Contributed by Mario Carneiro, 7-Oct-2016.)
Hypothesis
Ref Expression
mobidv.1 (𝜑 → (𝜓𝜒))
Assertion
Ref Expression
mobidv (𝜑 → (∃*𝑥𝜓 ↔ ∃*𝑥𝜒))
Distinct variable group:   𝜑,𝑥
Allowed substitution hints:   𝜓(𝑥)   𝜒(𝑥)

Proof of Theorem mobidv
StepHypRef Expression
1 nfv 1508 . 2 𝑥𝜑
2 mobidv.1 . 2 (𝜑 → (𝜓𝜒))
31, 2mobid 2041 1 (𝜑 → (∃*𝑥𝜓 ↔ ∃*𝑥𝜒))
 Colors of variables: wff set class Syntax hints:   → wi 4   ↔ wb 104  ∃*wmo 2007 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1427  ax-gen 1429  ax-ie1 1473  ax-ie2 1474  ax-4 1490  ax-17 1506  ax-ial 1514 This theorem depends on definitions:  df-bi 116  df-nf 1441  df-eu 2009  df-mo 2010 This theorem is referenced by:  mobii  2043  mosubopt  4648  dffun6f  5180  funmo  5182  1stconst  6162  2ndconst  6163  dvfgg  13017
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