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Theorem 19.3h 1540
Description: A wff may be quantified with a variable not free in it. Theorem 19.3 of [Margaris] p. 89. (Contributed by NM, 5-Aug-1993.) (Revised by NM, 21-May-2007.)
Hypothesis
Ref Expression
19.3h.1 (𝜑 → ∀𝑥𝜑)
Assertion
Ref Expression
19.3h (∀𝑥𝜑𝜑)

Proof of Theorem 19.3h
StepHypRef Expression
1 ax-4 1497 . 2 (∀𝑥𝜑𝜑)
2 19.3h.1 . 2 (𝜑 → ∀𝑥𝜑)
31, 2impbii 125 1 (∀𝑥𝜑𝜑)
Colors of variables: wff set class
Syntax hints:  wi 4  wb 104  wal 1340
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia2 106  ax-ia3 107  ax-4 1497
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  19.27h  1547  19.28h  1549  equsalh  1713  2eu4  2106
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