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Mirrors > Home > ILE Home > Th. List > hbth | Unicode version |
Description: No variable is
(effectively) free in a theorem.
This and later "hypothesis-building" lemmas, with labels starting "hb...", allow us to construct proofs of formulas of the form from smaller formulas of this form. These are useful for constructing hypotheses that state " is (effectively) not free in ." (Contributed by NM, 5-Aug-1993.) |
Ref | Expression |
---|---|
hbth.1 |
Ref | Expression |
---|---|
hbth |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | hbth.1 | . . 3 | |
2 | 1 | ax-gen 1335 | . 2 |
3 | 2 | a1i 9 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wal 1240 |
This theorem was proved from axioms: ax-1 5 ax-mp 7 ax-gen 1335 |
This theorem is referenced by: nfth 1350 sbieh 1670 bj-sbimeh 9247 |
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