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Theorem rmo2i 3132
 Description: Condition implying restricted "at most one." (Contributed by NM, 17-Jun-2017.)
Hypothesis
Ref Expression
rmo2.1 yφ
Assertion
Ref Expression
rmo2i (y A x A (φx = y) → ∃*x A φ)
Distinct variable group:   x,y,A
Allowed substitution hints:   φ(x,y)

Proof of Theorem rmo2i
StepHypRef Expression
1 rexex 2673 . 2 (y A x A (φx = y) → yx A (φx = y))
2 rmo2.1 . . 3 yφ
32rmo2 3131 . 2 (∃*x A φyx A (φx = y))
41, 3sylibr 203 1 (y A x A (φx = y) → ∃*x A φ)
 Colors of variables: wff setvar class Syntax hints:   → wi 4  ∃wex 1541  Ⅎwnf 1544  ∀wral 2614  ∃wrex 2615  ∃*wrmo 2617 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-eu 2208  df-mo 2209  df-ral 2619  df-rex 2620  df-rmo 2622 This theorem is referenced by: (None)
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