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Theorem pm11.71 36817
 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 1769 . . . 4
2 nfv 1769 . . . 4
31, 2aaan 2074 . . 3
4 prth 581 . . . 4
542alimi 1693 . . 3
63, 5sylbir 218 . 2
7 nfv 1769 . . . . . 6
87nfex 2050 . . . . 5
9 exim 1714 . . . . . . 7
10 19.42v 1842 . . . . . . 7
11 19.42v 1842 . . . . . . 7
129, 10, 113imtr3g 277 . . . . . 6
13 pm3.21 455 . . . . . . 7
14 simpl 464 . . . . . . . 8
1514imim2i 16 . . . . . . 7
1613, 15syl9 72 . . . . . 6
1712, 16syl5 32 . . . . 5
188, 17alimd 1974 . . . 4
20 ax-11 1937 . . . . 5
21 nfv 1769 . . . . . . 7
2221nfex 2050 . . . . . 6
23 exim 1714 . . . . . . . 8
24 19.41v 1838 . . . . . . . 8
25 19.41v 1838 . . . . . . . 8
2623, 24, 253imtr3g 277 . . . . . . 7
27 pm3.2 454 . . . . . . . 8
28 simpr 468 . . . . . . . . 9
2928imim2i 16 . . . . . . . 8
3027, 29syl9 72 . . . . . . 7
3126, 30syl5 32 . . . . . 6
3222, 31alimd 1974 . . . . 5
3320, 32syl5 32 . . . 4