NFE Home New Foundations Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  NFE Home  >  Th. List  >  2euswap Unicode version

Theorem 2euswap 2280
Description: A condition allowing swap of uniqueness and existential quantifiers. (Contributed by NM, 10-Apr-2004.)
Assertion
Ref Expression
2euswap

Proof of Theorem 2euswap
StepHypRef Expression
1 excomim 1742 . . . 4
21a1i 10 . . 3
3 2moswap 2279 . . 3
42, 3anim12d 546 . 2
5 eu5 2242 . 2
6 eu5 2242 . 2
74, 5, 63imtr4g 261 1
Colors of variables: wff setvar class
Syntax hints:   wi 4   wa 358  wal 1540  wex 1541  weu 2204  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
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
This theorem is referenced by:  euxfr2  3021  2reuswap  3038
  Copyright terms: Public domain W3C validator