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Theorem ax12vALT 2277
 Description: Alternate proof of ax12v 1951, shorter, but depending on more axioms. (Contributed by NM, 5-Aug-1993.) (New usage is discouraged.) (Proof modification is discouraged.)
Assertion
Ref Expression
ax12vALT
Distinct variable group:   ,
Allowed substitution hints:   (,)

Proof of Theorem ax12vALT
StepHypRef Expression
1 ax-1 6 . . . 4
2 axc16 2043 . . . 4
31, 2syl5 32 . . 3
43a1d 25 . 2
5 axc15 2153 . 2
64, 5pm2.61i 169 1
 Colors of variables: wff setvar class Syntax hints:   wi 4  wal 1450 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1677  ax-4 1690  ax-5 1766  ax-6 1813  ax-7 1859  ax-10 1932  ax-12 1950  ax-13 2104 This theorem depends on definitions:  df-bi 190  df-an 378  df-ex 1672  df-nf 1676 This theorem is referenced by: (None)
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