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Theorem axc16i 2064
Description: Inference with axc16 1941 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:   , ,   ,

Proof of Theorem axc16i
StepHypRef Expression
1 nfv 1707 . . 3
2 nfv 1707 . . 3
3 ax-7 1790 . . 3
41, 2, 3cbv3 2015 . 2
5 ax-7 1790 . . . . 5
65spimv 2009 . . . 4
7 equcomi 1793 . . . . . 6
8 equcomi 1793 . . . . . . 7
9 ax-7 1790 . . . . . . 7
108, 9syl 16 . . . . . 6
117, 10syl5com 30 . . . . 5
1211alimdv 1709 . . . 4
136, 12mpcom 36 . . 3
14 equcomi 1793 . . . 4
1514alimi 1633 . . 3
1613, 15syl 16 . 2
17 axc16i.1 . . . . 5
1817biimpcd 224 . . . 4
1918alimdv 1709 . . 3
20 axc16i.2 . . . . 5
2120nfi 1623 . . . 4
22 nfv 1707 . . . 4
2317biimprd 223 . . . . 5
2414, 23syl 16 . . . 4
2521, 22, 24cbv3 2015 . . 3
2619, 25syl6com 35 . 2
274, 16, 263syl 20 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  <->wb 184  A.wal 1393
This theorem is referenced by:  axc16ALT  2105
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
This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1613  df-nf 1617
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