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Theorem dtruALT2 4696
 Description: Alternate proof of dtru 4643 using ax-pr 4691 instead of ax-pow 4630. (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 4624 . . . 4
2 snex 4693 . . . . 5
3 eqeq2 2472 . . . . . 6
43notbid 294 . . . . 5
52, 4spcev 3201 . . . 4
61, 5syl 16 . . 3
7 0ex 4582 . . . 4
8 eqeq2 2472 . . . . 5
98notbid 294 . . . 4
107, 9spcev 3201 . . 3
116, 10pm2.61i 164 . 2
12 exnal 1648 . . 3
13 eqcom 2466 . . . 4
1413albii 1640 . . 3
1512, 14xchbinx 310 . 2
1611, 15mpbi 208 1
 Colors of variables: wff setvar class Syntax hints:  -.wn 3  A.wal 1393  =wceq 1395  E.wex 1612   c0 3784  {csn 4029 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-9 1822  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435  ax-sep 4573  ax-nul 4581  ax-pr 4691 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  df-v 3111  df-dif 3478  df-un 3480  df-nul 3785  df-sn 4030  df-pr 4032
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