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Theorem a16g 1945
 Description: Generalization of ax16 2045. (Contributed by NM, 25-Jul-2015.)
Assertion
Ref Expression
a16g
Distinct variable group:   ,
Allowed substitution hints:   (,,)

Proof of Theorem a16g
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 a9ev 1656 . 2
2 ax10lem5 1942 . 2
3 hbn1 1730 . . . . 5
4 pm2.21 100 . . . . 5
53, 4alrimih 1565 . . . 4
6 ax-17 1616 . . . . 5
7 ax-1 5 . . . . 5
86, 7alrimih 1565 . . . 4
95, 8ja 153 . . 3
10 ax10lem5 1942 . . . 4
11 equcomi 1679 . . . . . . 7
12 ax-17 1616 . . . . . . 7
13 ax-11 1746 . . . . . . 7
1411, 12, 13syl2im 34 . . . . . 6
15 ax-5 1557 . . . . . 6
1614, 15syl6 29 . . . . 5
1716com23 72 . . . 4
1810, 17syl5 28 . . 3
199, 18exlimih 1804 . 2
201, 2, 19mpsyl 59 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wi 4  wal 1540  wex 1541 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 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:  ax16  2045  a16gb  2050  a16nf  2051
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