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Theorem 2eu7 2290
Description: Two equivalent expressions for double existential uniqueness. (Contributed by NM, 19-Feb-2005.)
Assertion
Ref Expression
2eu7

Proof of Theorem 2eu7
StepHypRef Expression
1 nfe1 1732 . . . 4  F/
21nfeu 2220 . . 3  F/
32euan 2261 . 2
4 ancom 437 . . . . 5
54eubii 2213 . . . 4
6 nfe1 1732 . . . . 5  F/
76euan 2261 . . . 4
8 ancom 437 . . . 4
95, 7, 83bitri 262 . . 3
109eubii 2213 . 2
11 ancom 437 . 2
123, 10, 113bitr4ri 269 1
Colors of variables: wff setvar class
Syntax hints:   wb 176   wa 358  wex 1541  weu 2204
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:  2eu8  2291
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