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Theorem nfrmo 2786
 Description: Bound-variable hypothesis builder for restricted uniqueness. (Contributed by NM, 16-Jun-2017.)
Hypotheses
Ref Expression
nfreu.1 xA
nfreu.2 xφ
Assertion
Ref Expression
nfrmo x∃*y A φ

Proof of Theorem nfrmo
StepHypRef Expression
1 df-rmo 2622 . 2 (∃*y A φ∃*y(y A φ))
2 nftru 1554 . . . 4 y
3 nfcvf 2511 . . . . . . 7 x x = yxy)
4 nfreu.1 . . . . . . . 8 xA
54a1i 10 . . . . . . 7 x x = yxA)
63, 5nfeld 2504 . . . . . 6 x x = y → Ⅎx y A)
7 nfreu.2 . . . . . . 7 xφ
87a1i 10 . . . . . 6 x x = y → Ⅎxφ)
96, 8nfand 1822 . . . . 5 x x = y → Ⅎx(y A φ))
109adantl 452 . . . 4 (( ⊤ ¬ x x = y) → Ⅎx(y A φ))
112, 10nfmod2 2217 . . 3 ( ⊤ → Ⅎx∃*y(y A φ))
1211trud 1323 . 2 x∃*y(y A φ)
131, 12nfxfr 1570 1 x∃*y A φ
 Colors of variables: wff setvar class Syntax hints:  ¬ wn 3   ∧ wa 358   ⊤ wtru 1316  ∀wal 1540  Ⅎwnf 1544   ∈ wcel 1710  ∃*wmo 2205  Ⅎwnfc 2476  ∃*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  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-eu 2208  df-mo 2209  df-cleq 2346  df-clel 2349  df-nfc 2478  df-rmo 2622 This theorem is referenced by:  2rmorex  3040
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