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Theorem ax16i 2051
 Description: Inference with ax16 2050 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 1629 . . 3
2 nfv 1629 . . 3
3 ax-8 1687 . . 3
41, 2, 3cbv3 1971 . 2
5 ax-8 1687 . . . . 5
65spimv 1963 . . . 4
7 equcomi 1691 . . . . . 6
8 equcomi 1691 . . . . . . 7
9 ax-8 1687 . . . . . . 7
108, 9syl 16 . . . . . 6
117, 10syl5com 28 . . . . 5
1211alimdv 1631 . . . 4
136, 12mpcom 34 . . 3
14 equcomi 1691 . . . 4
1514alimi 1568 . . 3
1613, 15syl 16 . 2
17 ax16i.1 . . . . 5
1817biimpcd 216 . . . 4
1918alimdv 1631 . . 3
20 ax16i.2 . . . . 5
2120nfi 1560 . . . 4
22 nfv 1629 . . . 4
2317biimprd 215 . . . . 5
2414, 23syl 16 . . . 4
2521, 22, 24cbv3 1971 . . 3
2619, 25syl6com 33 . 2
274, 16, 263syl 19 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177  wal 1549 This theorem is referenced by:  ax16ALT  2154 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950 This theorem depends on definitions:  df-bi 178  df-an 361  df-ex 1551  df-nf 1554
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