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Theorem axinfprim 30341
 Description: ax-inf 8152 without distinct variable conditions or defined symbols. (New usage is discouraged.) (Contributed by Scott Fenton, 13-Oct-2010.)
Assertion
Ref Expression
axinfprim

Proof of Theorem axinfprim
StepHypRef Expression
1 axinfnd 9038 . 2
2 df-an 372 . . . . . . . . . . 11
32exbii 1712 . . . . . . . . . 10
4 exnal 1693 . . . . . . . . . 10
53, 4bitri 252 . . . . . . . . 9
65imbi2i 313 . . . . . . . 8
76albii 1685 . . . . . . 7
87anbi2i 698 . . . . . 6
9 df-an 372 . . . . . 6
108, 9bitri 252 . . . . 5
1110imbi2i 313 . . . 4
1211exbii 1712 . . 3
13 df-ex 1658 . . 3
1412, 13bitri 252 . 2
151, 14mpbi 211 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wi 4   wa 370  wal 1435  wex 1657 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1663  ax-4 1676  ax-5 1752  ax-6 1798  ax-7 1843  ax-8 1874  ax-9 1876  ax-10 1891  ax-11 1896  ax-12 1909  ax-13 2057  ax-ext 2401  ax-sep 4546  ax-nul 4555  ax-pr 4660  ax-reg 8116  ax-inf 8152 This theorem depends on definitions:  df-bi 188  df-or 371  df-an 372  df-tru 1440  df-ex 1658  df-nf 1662  df-sb 1791  df-clab 2408  df-cleq 2414  df-clel 2417  df-nfc 2568  df-ne 2616  df-ral 2776  df-rex 2777  df-v 3082  df-dif 3439  df-un 3441  df-nul 3762  df-sn 3999  df-pr 4001 This theorem is referenced by: (None)
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