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Theorem pm14.24 26799
 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 2124 . . . . 5
2 nfsbc1v 2940 . . . . 5
3 pm14.12 26788 . . . . . . . . . 10
4319.21bbi 1775 . . . . . . . . 9
54ancomsd 442 . . . . . . . 8
65expdimp 428 . . . . . . 7
7 pm13.13b 26775 . . . . . . . . . 10
87expcom 426 . . . . . . . . 9
98com12 29 . . . . . . . 8
109adantl 454 . . . . . . 7
116, 10impbid 185 . . . . . 6
1211ex 425 . . . . 5
131, 2, 12alrimd 1710 . . . 4
14 iotaval 6154 . . . . 5
1514eqcomd 2258 . . . 4
1613, 15syl6 31 . . 3
17 iota4 6161 . . . 4
18 dfsbcq 2923 . . . 4
1917, 18syl5ibrcom 215 . . 3
2016, 19impbid 185 . 2
2120alrimiv 2012 1
 Colors of variables: wff set class Syntax hints:   wi 6   wb 178   wa 360  wal 1532   wceq 1619  weu 2114  wsbc 2921  cio 6141 This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-6 1534  ax-7 1535  ax-gen 1536  ax-8 1623  ax-11 1624  ax-17 1628  ax-12o 1664  ax-10 1678  ax-9 1684  ax-4 1692  ax-16 1926  ax-ext 2234 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1315  df-ex 1538  df-nf 1540  df-sb 1883  df-eu 2118  df-mo 2119  df-clab 2240  df-cleq 2246  df-clel 2249  df-nfc 2374  df-rex 2514  df-v 2729  df-sbc 2922  df-un 3083  df-sn 3550  df-pr 3551  df-uni 3728  df-iota 6143
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