Intuitionistic Logic Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  ILE Home  >  Th. List  >  ax11i Unicode version

Theorem ax11i 1643
 Description: Inference that has ax-11 1438 (without ) as its conclusion and doesn't require ax-10 1437, ax-11 1438, or ax-12 1443 for its proof. The hypotheses may be eliminable without one or more of these axioms in special cases. Proof similar to Lemma 16 of [Tarski] p. 70. (Contributed by NM, 20-May-2008.)
Hypotheses
Ref Expression
ax11i.1
ax11i.2
Assertion
Ref Expression
ax11i

Proof of Theorem ax11i
StepHypRef Expression
1 ax11i.1 . 2
2 ax11i.2 . . 3
31biimprcd 158 . . 3
42, 3alrimih 1399 . 2
51, 4syl6bi 161 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 103  wal 1283 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1377  ax-gen 1379 This theorem depends on definitions:  df-bi 115 This theorem is referenced by: (None)
 Copyright terms: Public domain W3C validator