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Theorem e2ebindALT 29041
 Description: Absorption of an existential quantifier of a double existential quantifier of non-distinct variables. The proof is derived by completeusersproof.c from User's Proof in VirtualDeductionProofs.txt. The User's Proof in html format is displayed in e2ebindVD 29024. (Contributed by Alan Sare, 11-Sep-2016.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
e2ebindALT

Proof of Theorem e2ebindALT
StepHypRef Expression
1 ax10 2025 . 2
2 nfe1 1747 . . . 4
3219.9 1797 . . 3
4 excom 1756 . . . 4
5 nfa1 1806 . . . . . 6
6 id 20 . . . . . . 7
7 biid 228 . . . . . . . . 9
87a1i 11 . . . . . . . 8
98drex1 2059 . . . . . . 7
106, 9syl 16 . . . . . 6
115, 10alrimi 1781 . . . . 5
12 exbi 1591 . . . . 5
1311, 12syl 16 . . . 4
14 wl-bitr1 26220 . . . . 5
1514impcom 420 . . . 4
164, 13, 15sylancr 645 . . 3
17 bitr3 28593 . . . 4
1817impcom 420 . . 3
193, 16, 18sylancr 645 . 2
201, 19syl 16 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177  wal 1549  wex 1550   wceq 1652 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-an 361  df-ex 1551  df-nf 1554
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