Mathbox for Andrew Salmon < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  ax4567to6 Structured version   Unicode version

Theorem ax4567to6 27581
 Description: Re-derivation of ax6o 1766 from ax4567 27578. Note that neither ax6o 1766 nor ax-7 1749 are required for the re-derivation. (Contributed by Andrew Salmon, 14-Jul-2011.) (Proof modification is discouraged.)
Assertion
Ref Expression
ax4567to6

Proof of Theorem ax4567to6
StepHypRef Expression
1 ax-1 5 . . . . . . . 8
21alimi 1568 . . . . . . 7
32a5i 1807 . . . . . 6
43con3i 129 . . . . 5
54alimi 1568 . . . 4
65sps 1770 . . 3
76con3i 129 . 2
8 pm2.21 102 . . . 4
9 ax4567 27578 . . . 4
108, 9syl 16 . . 3
11 sp 1763 . . 3
1210, 11syl6 31 . 2
13 pm2.27 37 . . 3
14 id 20 . . 3
1513, 14mpg 1557 . 2
167, 12, 153syl 19 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4  wal 1549 This theorem is referenced by:  ax4567to7  27582 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-6 1744  ax-7 1749  ax-11 1761 This theorem depends on definitions:  df-bi 178  df-ex 1551  df-nf 1554
 Copyright terms: Public domain W3C validator