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Theorem aev-o 2261
Description: A "distinctor elimination" lemma with no restrictions on variables in the consequent, proved without using ax-c16 2223. Version of aev 1943 using ax-c11 2218. (Contributed by NM, 8-Nov-2006.) (Proof shortened by Andrew Salmon, 21-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
aev-o
Distinct variable group:   ,

Proof of Theorem aev-o
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 hbae-o 2232 . 2
2 hbae-o 2232 . . . 4
3 ax-7 1790 . . . . 5
43spimv 2009 . . . 4
52, 4alrimih 1642 . . 3
6 ax-7 1790 . . . . . . . 8
7 equcomi 1793 . . . . . . . 8
86, 7syl6 33 . . . . . . 7
98spimv 2009 . . . . . 6
109aecoms-o 2231 . . . . 5
1110axc4i-o 2229 . . . 4
12 hbae-o 2232 . . . . 5
13 ax-7 1790 . . . . . 6
1413spimv 2009 . . . . 5
1512, 14alrimih 1642 . . . 4
16 aecom-o 2230 . . . 4
1711, 15, 163syl 20 . . 3
18 ax-7 1790 . . . 4
1918spimv 2009 . . 3
205, 17, 193syl 20 . 2
211, 20alrimih 1642 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  A.wal 1393
This theorem is referenced by:  ax16g-o  2264
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-c5 2214  ax-c4 2215  ax-c7 2216  ax-c11 2218  ax-c9 2221
This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1613  df-nf 1617
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