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Theorem axc16i 2171
 Description: Inference with axc16 2043 as its conclusion. (Contributed by NM, 20-May-2008.) (Proof modification is discouraged.)
Hypotheses
Ref Expression
axc16i.1
axc16i.2
Assertion
Ref Expression
axc16i
Distinct variable groups:   ,,   ,
Allowed substitution hints:   (,)   (,,)

Proof of Theorem axc16i
StepHypRef Expression
1 nfv 1769 . . 3
2 nfv 1769 . . 3
3 ax7 1868 . . 3
41, 2, 3cbv3 2121 . 2
5 ax7 1868 . . . . 5
65spimv 2114 . . . 4
7 equcomi 1869 . . . . . 6
8 equcomi 1869 . . . . . . 7
9 ax7 1868 . . . . . . 7
108, 9syl 17 . . . . . 6
117, 10syl5com 30 . . . . 5
1211alimdv 1771 . . . 4
136, 12mpcom 36 . . 3
14 equcomi 1869 . . . 4
1514alimi 1692 . . 3
1613, 15syl 17 . 2
17 axc16i.1 . . . . 5
1817biimpcd 232 . . . 4
1918alimdv 1771 . . 3
20 axc16i.2 . . . . 5
2120nfi 1682 . . . 4
22 nfv 1769 . . . 4
2317biimprd 231 . . . . 5
2414, 23syl 17 . . . 4
2521, 22, 24cbv3 2121 . . 3
2619, 25syl6com 35 . 2
274, 16, 263syl 18 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 189  wal 1450 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1677  ax-4 1690  ax-5 1766  ax-6 1813  ax-7 1859  ax-10 1932  ax-11 1937  ax-12 1950  ax-13 2104 This theorem depends on definitions:  df-bi 190  df-an 378  df-ex 1672  df-nf 1676 This theorem is referenced by:  axc16ALT  2215
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