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Theorem mobidv 1985
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 1467 . 2 𝑥𝜑
2 mobidv.1 . 2 (𝜑 → (𝜓𝜒))
31, 2mobid 1984 1 (𝜑 → (∃*𝑥𝜓 ↔ ∃*𝑥𝜒))
Colors of variables: wff set class
Syntax hints:  wi 4  wb 104  ∃*wmo 1950
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1382  ax-gen 1384  ax-ie1 1428  ax-ie2 1429  ax-4 1446  ax-17 1465  ax-ial 1473
This theorem depends on definitions:  df-bi 116  df-nf 1396  df-eu 1952  df-mo 1953
This theorem is referenced by:  mobii  1986  mosubopt  4518  dffun6f  5043  funmo  5045  1stconst  6002  2ndconst  6003
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