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Theorem ax16i 2046
 Description: Inference with ax16 2045 as its conclusion. (Contributed by NM, 20-May-2008.) (Proof modification is discouraged.)
Hypotheses
Ref Expression
ax16i.1
ax16i.2
Assertion
Ref Expression
ax16i
Distinct variable groups:   ,,   ,
Allowed substitution hints:   (,)   (,,)

Proof of Theorem ax16i
StepHypRef Expression
1 nfv 1619 . . 3
2 nfv 1619 . . 3
3 ax-8 1675 . . 3
41, 2, 3cbv3 1982 . 2
5 ax-8 1675 . . . . 5
65spimv 1990 . . . 4
7 equcomi 1679 . . . . . 6
8 equcomi 1679 . . . . . . 7
9 ax-8 1675 . . . . . . 7
108, 9syl 15 . . . . . 6
117, 10syl5com 26 . . . . 5
1211alimdv 1621 . . . 4
136, 12mpcom 32 . . 3
14 equcomi 1679 . . . 4
1514alimi 1559 . . 3
1613, 15syl 15 . 2
17 ax16i.1 . . . . 5
1817biimpcd 215 . . . 4
1918alimdv 1621 . . 3
20 ax16i.2 . . . . 5
2120nfi 1551 . . . 4
22 nfv 1619 . . . 4
2317biimprd 214 . . . . 5
2414, 23syl 15 . . . 4
2521, 22, 24cbv3 1982 . . 3
2619, 25syl6com 31 . 2
274, 16, 263syl 18 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 176  wal 1540 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 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:  ax16ALT  2047
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