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Mirrors > Home > ILE Home > Th. List > ax11i | Unicode version |
Description: Inference that has ax-11 1437 (without ) as its conclusion and doesn't require ax-10 1436, ax-11 1437, or ax-12 1442 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.) |
Ref | Expression |
---|---|
ax11i.1 | |
ax11i.2 |
Ref | Expression |
---|---|
ax11i |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax11i.1 | . 2 | |
2 | ax11i.2 | . . 3 | |
3 | 1 | biimprcd 158 | . . 3 |
4 | 2, 3 | alrimih 1398 | . 2 |
5 | 1, 4 | syl6bi 161 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 103 wal 1282 |
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 1376 ax-gen 1378 |
This theorem depends on definitions: df-bi 115 |
This theorem is referenced by: (None) |
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