Mathbox for Andrew Salmon < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  pm11.71 Unicode version

Theorem pm11.71 27596
 Description: Theorem *11.71 in [WhiteheadRussell] p. 166. (Contributed by Andrew Salmon, 24-May-2011.)
Assertion
Ref Expression
pm11.71
Distinct variable groups:   ,   ,   ,   ,
Allowed substitution hints:   ()   ()   ()   ()

Proof of Theorem pm11.71
StepHypRef Expression
1 nfv 1605 . . . 4
2 nfv 1605 . . . 4
31, 2aaan 1825 . . 3
4 prth 554 . . . 4
542alimi 1547 . . 3
63, 5sylbir 204 . 2
7 nfv 1605 . . . . . 6
87nfex 1767 . . . . 5
9 exim 1562 . . . . . . 7
10 19.42v 1846 . . . . . . 7
11 19.42v 1846 . . . . . . 7
129, 10, 113imtr3g 260 . . . . . 6
13 pm3.21 435 . . . . . . 7
14 simpl 443 . . . . . . . 8
1514imim2i 13 . . . . . . 7
1613, 15syl9 66 . . . . . 6
1712, 16syl5 28 . . . . 5
188, 17alimd 1744 . . . 4
1918adantl 452 . . 3
20 ax-7 1708 . . . . 5
21 nfv 1605 . . . . . . 7
2221nfex 1767 . . . . . 6
23 exim 1562 . . . . . . . 8
24 19.41v 1842 . . . . . . . 8
25 19.41v 1842 . . . . . . . 8
2623, 24, 253imtr3g 260 . . . . . . 7
27 pm3.2 434 . . . . . . . 8
28 simpr 447 . . . . . . . . 9
2928imim2i 13 . . . . . . . 8
3027, 29syl9 66 . . . . . . 7
3126, 30syl5 28 . . . . . 6
3222, 31alimd 1744 . . . . 5
3320, 32syl5 28 . . . 4
3433adantr 451 . . 3
3519, 34jcad 519 . 2
366, 35impbid2 195 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 176   wa 358  wal 1527  wex 1528 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715 This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1310  df-ex 1529  df-nf 1532
 Copyright terms: Public domain W3C validator