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Theorem ax4567to4 27914
Description: Re-derivation of sp 1766 from ax4567 27913. Note that ax9 1958 is used for the re-derivation. (Contributed by Andrew Salmon, 14-Jul-2011.) (Proof modification is discouraged.)
Assertion
Ref Expression
ax4567to4

Proof of Theorem ax4567to4
StepHypRef Expression
1 ax9 1958 . . 3
2 pm2.21 103 . . . 4
3 ax-1 6 . . . 4
4 ax4567 27913 . . . 4
52, 3, 43syl 19 . . 3
61, 5mtoi 172 . 2
76con4i 125 1
Colors of variables: wff set class
Syntax hints:  -.wn 3  ->wi 4  A.wal 1550  =wceq 1654
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1628  ax-9 1669  ax-8 1690  ax-6 1747  ax-7 1752  ax-11 1764  ax-12 1955
This theorem depends on definitions:  df-bi 179  df-an 362  df-ex 1552
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