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Theorem pm14.24 27609
 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 2291 . . . . 5
2 nfsbc1v 3180 . . . . 5
3 pm14.12 27598 . . . . . . . . . 10
4319.21bbi 1888 . . . . . . . . 9
54ancomsd 441 . . . . . . . 8
65expdimp 427 . . . . . . 7
7 pm13.13b 27585 . . . . . . . . 9
87ex 424 . . . . . . . 8
98adantl 453 . . . . . . 7
106, 9impbid 184 . . . . . 6
1110ex 424 . . . . 5
121, 2, 11alrimd 1785 . . . 4
13 iotaval 5429 . . . . 5
1413eqcomd 2441 . . . 4
1512, 14syl6 31 . . 3
16 iota4 5436 . . . 4
17 dfsbcq 3163 . . . 4
1816, 17syl5ibrcom 214 . . 3
1915, 18impbid 184 . 2
2019alrimiv 1641 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wa 359  wal 1549   wceq 1652  weu 2281  wsbc 3161  cio 5416 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-eu 2285  df-mo 2286  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-rex 2711  df-v 2958  df-sbc 3162  df-un 3325  df-sn 3820  df-pr 3821  df-uni 4016  df-iota 5418
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