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Theorem dtruALT2 4658
 Description: Alternate proof of dtru 4608 using ax-pr 4653 instead of ax-pow 4595. (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 4589 . . . 4
2 snex 4655 . . . . 5
3 eqeq2 2435 . . . . . 6
43notbid 295 . . . . 5
52, 4spcev 3170 . . . 4
61, 5syl 17 . . 3
7 0ex 4549 . . . 4
8 eqeq2 2435 . . . . 5
98notbid 295 . . . 4
107, 9spcev 3170 . . 3
116, 10pm2.61i 167 . 2
12 exnal 1695 . . 3
13 eqcom 2429 . . . 4
1413albii 1687 . . 3
1512, 14xchbinx 311 . 2
1611, 15mpbi 211 1
 Colors of variables: wff setvar class Syntax hints:   wn 3  wal 1435   wceq 1437  wex 1659  c0 3758  csn 3993 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1665  ax-4 1678  ax-5 1748  ax-6 1794  ax-7 1838  ax-9 1871  ax-10 1886  ax-11 1891  ax-12 1904  ax-13 2052  ax-ext 2398  ax-sep 4540  ax-nul 4548  ax-pr 4653 This theorem depends on definitions:  df-bi 188  df-or 371  df-an 372  df-tru 1440  df-ex 1660  df-nf 1664  df-sb 1787  df-clab 2406  df-cleq 2412  df-clel 2415  df-nfc 2570  df-ne 2618  df-v 3080  df-dif 3436  df-un 3438  df-nul 3759  df-sn 3994  df-pr 3996 This theorem is referenced by: (None)
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