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Theorem mosub 3014
 Description: "At most one" remains true after substitution. (Contributed by NM, 9-Mar-1995.)
Hypothesis
Ref Expression
mosub.1 ∃*xφ
Assertion
Ref Expression
mosub ∃*xy(y = A φ)
Distinct variable group:   x,y,A
Allowed substitution hints:   φ(x,y)

Proof of Theorem mosub
StepHypRef Expression
1 moeq 3012 . 2 ∃*y y = A
2 mosub.1 . . 3 ∃*xφ
32ax-gen 1546 . 2 y∃*xφ
4 moexexv 2274 . 2 ((∃*y y = A y∃*xφ) → ∃*xy(y = A φ))
51, 3, 4mp2an 653 1 ∃*xy(y = A φ)
 Colors of variables: wff setvar class Syntax hints:   ∧ wa 358  ∀wal 1540  ∃wex 1541   = wceq 1642  ∃*wmo 2205 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-or 359  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-eu 2208  df-mo 2209  df-clab 2340  df-cleq 2346  df-clel 2349  df-v 2861 This theorem is referenced by: (None)
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