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Theorem 2eu1 2360
 Description: Double existential uniqueness. This theorem shows a condition under which a "naive" definition matches the correct one. (Contributed by NM, 3-Dec-2001.)
Assertion
Ref Expression
2eu1

Proof of Theorem 2eu1
StepHypRef Expression
1 eu5 2318 . . . . . . . 8
2 eu5 2318 . . . . . . . . . 10
32exbii 1592 . . . . . . . . 9
42mobii 2316 . . . . . . . . 9
53, 4anbi12i 679 . . . . . . . 8
61, 5bitri 241 . . . . . . 7
76simprbi 451 . . . . . 6
8 sp 1763 . . . . . . . . . . . 12
98anim2i 553 . . . . . . . . . . 11
109ancoms 440 . . . . . . . . . 10
1110moimi 2327 . . . . . . . . 9
12 nfa1 1806 . . . . . . . . . 10
1312moanim 2336 . . . . . . . . 9
1411, 13sylib 189 . . . . . . . 8
1514ancrd 538 . . . . . . 7
16 2moswap 2355 . . . . . . . . 9
1716com12 29 . . . . . . . 8
1817imdistani 672 . . . . . . 7
1915, 18syl6 31 . . . . . 6
207, 19syl 16 . . . . 5
21 2eu2ex 2354 . . . . . 6
22 excom 1756 . . . . . . 7
2321, 22sylib 189 . . . . . 6
2421, 23jca 519 . . . . 5
2520, 24jctild 528 . . . 4
26 eu5 2318 . . . . . 6
27 eu5 2318 . . . . . 6
2826, 27anbi12i 679 . . . . 5
29 an4 798 . . . . 5
3028, 29bitri 241 . . . 4
3125, 30syl6ibr 219 . . 3
3231com12 29 . 2
33 2exeu 2357 . 2
3432, 33impbid1 195 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wa 359  wal 1549  wex 1550  weu 2280  wmo 2281 This theorem is referenced by:  2eu2  2361  2eu3  2362  2eu5  2364 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-eu 2284  df-mo 2285
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