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Theorem ax-12 1272
Description: Rederive the original version of the axiom from ax-i12 1270. Note that we need ax-4 1271 for the derivation, but the proof of ax4 1808 is nontheless non-circular since it does not use ax-12. (Contributed by Mario Carneiro, 3-Feb-2015.)
Assertion
Ref Expression
ax-12

Proof of Theorem ax-12
StepHypRef Expression
1 ax-i12 1270 . . . 4
21ori 617 . . 3
32ord 618 . 2
4 ax-4 1271 . 2
53, 4syl6 27 1
Colors of variables: wff set class
Syntax hints:   wn 3   wi 4   wo 605  wal 1214   wceq 1262
This theorem is referenced by:  dvelimfALT  1417  ax17eq  1482  hbsb4  1525  sbcom  1535  dvelimALT  1653  ax11eq  1810  ax11indalem  1814  a12stdy4  1821  a12lem1  1822
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 97  ax-ia2 98  ax-ia3 99  ax-in2 527  ax-io 606  ax-i12 1270  ax-4 1271
This theorem depends on definitions:  df-bi 108
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