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Theorem pm14.24 27735
 Description: Theorem *14.24 in [WhiteheadRussell] p. 191. (Contributed by Andrew Salmon, 12-Jul-2011.)
Assertion
Ref Expression
pm14.24
Distinct variable groups:   ,   ,
Allowed substitution hint:   ()

Proof of Theorem pm14.24
StepHypRef Expression
1 nfeu1 2166 . . . . 5
2 nfsbc1v 3023 . . . . 5
3 pm14.12 27724 . . . . . . . . . 10
4319.21bbi 1807 . . . . . . . . 9
54ancomsd 440 . . . . . . . 8
65expdimp 426 . . . . . . 7
7 pm13.13b 27711 . . . . . . . . . 10
87expcom 424 . . . . . . . . 9
98com12 27 . . . . . . . 8
109adantl 452 . . . . . . 7
116, 10impbid 183 . . . . . 6
1211ex 423 . . . . 5
131, 2, 12alrimd 1761 . . . 4
14 iotaval 5246 . . . . 5
1514eqcomd 2301 . . . 4
1613, 15syl6 29 . . 3
17 iota4 5253 . . . 4
18 dfsbcq 3006 . . . 4
1917, 18syl5ibrcom 213 . . 3
2016, 19impbid 183 . 2
2120alrimiv 1621 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 176   wa 358  wal 1530   wceq 1632  weu 2156  wsbc 3004  cio 5233 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-eu 2160  df-mo 2161  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-rex 2562  df-v 2803  df-sbc 3005  df-un 3170  df-sn 3659  df-pr 3660  df-uni 3844  df-iota 5235
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