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Theorem pm11.71 26762
 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 1629 . . . 4
2 nfv 1629 . . . 4
31, 2aaan 1811 . . 3
4 prth 557 . . . 4
542alimi 1547 . . 3
63, 5sylbir 206 . 2
7 nfv 1629 . . . . . 6
87nfex 1733 . . . . 5
9 exim 1573 . . . . . . 7
10 19.42v 2038 . . . . . . 7
11 19.42v 2038 . . . . . . 7
129, 10, 113imtr3g 262 . . . . . 6
13 pm3.21 437 . . . . . . 7
14 simpl 445 . . . . . . . 8
1514imim2i 15 . . . . . . 7
1613, 15syl9 68 . . . . . 6
1712, 16syl5 30 . . . . 5
188, 17alimd 1705 . . . 4
20 ax-7 1535 . . . . 5
21 nfv 1629 . . . . . . 7
2221nfex 1733 . . . . . 6
23 exim 1573 . . . . . . . 8
24 19.41v 2034 . . . . . . . 8
25 19.41v 2034 . . . . . . . 8
2623, 24, 253imtr3g 262 . . . . . . 7
27 pm3.2 436 . . . . . . . 8
28 simpr 449 . . . . . . . . 9
2928imim2i 15 . . . . . . . 8
3027, 29syl9 68 . . . . . . 7
3126, 30syl5 30 . . . . . 6
3222, 31alimd 1705 . . . . 5
3320, 32syl5 30 . . . 4