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Theorem hbth 1624
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 |-( ->A.x ) 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.)

Hypothesis
Ref Expression
hbth.1
Assertion
Ref Expression
hbth

Proof of Theorem hbth
StepHypRef Expression
1 hbth.1 . . 3
21ax-gen 1618 . 2
32a1i 11 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  A.wal 1393
This theorem is referenced by:  nfth  1625  spfalw  1786
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-gen 1618
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