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Theorem dtruALT2 4408
 Description: An alternative proof of dtru 4390 ("two things exist") using ax-pr 4403 instead of ax-pow 4377. (Contributed by Mario Carneiro, 31-Aug-2015.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
dtruALT2
Distinct variable group:   ,

Proof of Theorem dtruALT2
StepHypRef Expression
1 0inp0 4371 . . . 4
2 snex 4405 . . . . 5
3 eqeq2 2445 . . . . . 6
43notbid 286 . . . . 5
52, 4spcev 3043 . . . 4
61, 5syl 16 . . 3
7 0ex 4339 . . . 4
8 eqeq2 2445 . . . . 5
98notbid 286 . . . 4
107, 9spcev 3043 . . 3
116, 10pm2.61i 158 . 2
12 exnal 1583 . . 3
13 eqcom 2438 . . . 4
1413albii 1575 . . 3
1512, 14xchbinx 302 . 2
1611, 15mpbi 200 1
 Colors of variables: wff set class Syntax hints:   wn 3  wal 1549  wex 1550   wceq 1652  c0 3628  csn 3814 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-14 1729  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417  ax-sep 4330  ax-nul 4338  ax-pr 4403 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-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-ne 2601  df-v 2958  df-dif 3323  df-un 3325  df-nul 3629  df-sn 3820  df-pr 3821
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