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Theorem aev-o 32471
 Description: A "distinctor elimination" lemma with no restrictions on variables in the consequent, proved without using ax-c16 32433. Version of aev 2003 using ax-c11 32428. (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 32442 . 2
2 hbae-o 32442 . . . 4
3 ax-7 1843 . . . . 5
43spimv 2067 . . . 4
52, 4alrimih 1687 . . 3
6 ax-7 1843 . . . . . . . 8
7 equcomi 1847 . . . . . . . 8
86, 7syl6 34 . . . . . . 7
98spimv 2067 . . . . . 6
109aecoms-o 32441 . . . . 5
1110axc4i-o 32439 . . . 4
12 hbae-o 32442 . . . . 5
13 ax-7 1843 . . . . . 6
1413spimv 2067 . . . . 5
1512, 14alrimih 1687 . . . 4
16 aecom-o 32440 . . . 4
1711, 15, 163syl 18 . . 3
18 ax-7 1843 . . . 4
1918spimv 2067 . . 3
205, 17, 193syl 18 . 2
211, 20alrimih 1687 1
 Colors of variables: wff setvar class Syntax hints:   wi 4  wal 1435 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1663  ax-4 1676  ax-5 1752  ax-6 1798  ax-7 1843  ax-10 1891  ax-11 1896  ax-12 1909  ax-13 2057  ax-c5 32424  ax-c4 32425  ax-c7 32426  ax-c11 32428  ax-c9 32431 This theorem depends on definitions:  df-bi 188  df-an 372  df-ex 1658  df-nf 1662 This theorem is referenced by:  axc16g-o  32474
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