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Theorem pm14.24 36853
 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 2329 . . . . 5
2 nfsbc1v 3275 . . . . 5
3 pm14.12 36842 . . . . . . . . . 10
4319.21bbi 1968 . . . . . . . . 9
54ancomsd 461 . . . . . . . 8
65expdimp 444 . . . . . . 7
7 pm13.13b 36829 . . . . . . . . 9
87ex 441 . . . . . . . 8
98adantl 473 . . . . . . 7
106, 9impbid 195 . . . . . 6
1110ex 441 . . . . 5
121, 2, 11alrimd 1979 . . . 4
13 iotaval 5564 . . . . 5
1413eqcomd 2477 . . . 4
1512, 14syl6 33 . . 3
16 iota4 5571 . . . 4
17 dfsbcq 3257 . . . 4
1816, 17syl5ibrcom 230 . . 3
1915, 18impbid 195 . 2
2019alrimiv 1781 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 189   wa 376  wal 1450   wceq 1452  weu 2319  wsbc 3255  cio 5551 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1677  ax-4 1690  ax-5 1766  ax-6 1813  ax-7 1859  ax-10 1932  ax-11 1937  ax-12 1950  ax-13 2104  ax-ext 2451 This theorem depends on definitions:  df-bi 190  df-or 377  df-an 378  df-tru 1455  df-ex 1672  df-nf 1676  df-sb 1806  df-eu 2323  df-mo 2324  df-clab 2458  df-cleq 2464  df-clel 2467  df-nfc 2601  df-rex 2762  df-v 3033  df-sbc 3256  df-un 3395  df-sn 3960  df-pr 3962  df-uni 4191  df-iota 5553 This theorem is referenced by: (None)
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