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Theorem axinfprim 25155
 Description: ax-inf 7593 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 8481 . 2
2 df-an 361 . . . . . . . . . . 11
32exbii 1592 . . . . . . . . . 10
4 exnal 1583 . . . . . . . . . 10
53, 4bitri 241 . . . . . . . . 9
65imbi2i 304 . . . . . . . 8
76albii 1575 . . . . . . 7
87anbi2i 676 . . . . . 6
9 df-an 361 . . . . . 6
108, 9bitri 241 . . . . 5
1110imbi2i 304 . . . 4
1211exbii 1592 . . 3
13 df-ex 1551 . . 3
1412, 13bitri 241 . 2
151, 14mpbi 200 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wa 359  wal 1549  wex 1550 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-13 1727  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  ax-reg 7560  ax-inf 7593 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-ral 2710  df-rex 2711  df-v 2958  df-dif 3323  df-un 3325  df-nul 3629  df-sn 3820  df-pr 3821
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