Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > MPE Home > Th. List > hbth | Structured version Visualization version 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, 11-May-1993.) |
Ref | Expression |
---|---|
hbth.1 |
Ref | Expression |
---|---|
hbth |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | hbth.1 | . . 3 | |
2 | 1 | ax-gen 1677 | . 2 |
3 | 2 | a1i 11 | 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-gen 1677 |
This theorem is referenced by: nfth 1684 spfalw 1853 |
Copyright terms: Public domain | W3C validator |