New Foundations Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  NFE Home  >  Th. List  >  aev-o Unicode version

Theorem aev-o 2182
 Description: A "distinctor elimination" lemma with no restrictions on variables in the consequent, proved without using ax-16 2144. Version of aev 1991 using ax-10o 2139. (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 2153 . 2
2 hbae-o 2153 . . . 4
3 ax-8 1675 . . . . 5
43spimv 1990 . . . 4
52, 4alrimih 1565 . . 3
6 ax-8 1675 . . . . . . . 8
7 equcomi 1679 . . . . . . . 8
86, 7syl6 29 . . . . . . 7
98spimv 1990 . . . . . 6
109aecoms-o 2152 . . . . 5
1110a5i-o 2150 . . . 4
12 hbae-o 2153 . . . . 5
13 ax-8 1675 . . . . . 6
1413spimv 1990 . . . . 5
1512, 14alrimih 1565 . . . 4
16 aecom-o 2151 . . . 4
1711, 15, 163syl 18 . . 3
18 ax-8 1675 . . . 4
1918spimv 1990 . . 3
205, 17, 193syl 18 . 2
211, 20alrimih 1565 1
 Colors of variables: wff setvar class Syntax hints:   wi 4  wal 1540 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 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  ax-4 2135  ax-5o 2136  ax-6o 2137  ax-10o 2139  ax-12o 2142 This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545 This theorem is referenced by:  a16g-o  2186
 Copyright terms: Public domain W3C validator