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Theorem 19.3 2107
Description: A wff may be quantified with a variable not free in it. Theorem 19.3 of [Margaris] p. 89. See 19.3v 1954 for a version requiring fewer axioms. (Contributed by NM, 12-Mar-1993.) (Revised by Mario Carneiro, 24-Sep-2016.)
Hypothesis
Ref Expression
19.3.1 𝑥𝜑
Assertion
Ref Expression
19.3 (∀𝑥𝜑𝜑)

Proof of Theorem 19.3
StepHypRef Expression
1 sp 2091 . 2 (∀𝑥𝜑𝜑)
2 19.3.1 . . 3 𝑥𝜑
32nf5ri 2103 . 2 (𝜑 → ∀𝑥𝜑)
41, 3impbii 199 1 (∀𝑥𝜑𝜑)
Colors of variables: wff setvar class
Syntax hints:  wb 196  wal 1521  wnf 1748
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1762  ax-4 1777  ax-5 1879  ax-6 1945  ax-7 1981  ax-12 2087
This theorem depends on definitions:  df-bi 197  df-ex 1745  df-nf 1750
This theorem is referenced by:  19.16  2131  19.17  2132  19.27  2133  19.28  2134  19.37  2138  axrep4  4808  zfcndrep  9474  bj-alexbiex  32815  bj-alalbial  32817  bj-axrep4  32916
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