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Theorem 19.3 2131
 Description: A wff may be quantified with a variable not free in it. Version of 19.9 2134 with a universal quantifier. Theorem 19.3 of [Margaris] p. 89. See 19.3v 1939 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 2111 . 2 (∀𝑥𝜑𝜑)
2 19.3.1 . . 3 𝑥𝜑
32nf5ri 2123 . 2 (𝜑 → ∀𝑥𝜑)
41, 3impbii 201 1 (∀𝑥𝜑𝜑)
 Colors of variables: wff setvar class Syntax hints:   ↔ wb 198  ∀wal 1505  Ⅎwnf 1746 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1758  ax-4 1772  ax-5 1869  ax-6 1928  ax-7 1965  ax-12 2106 This theorem depends on definitions:  df-bi 199  df-ex 1743  df-nf 1747 This theorem is referenced by:  19.16  2157  19.17  2158  19.27  2159  19.28  2160  19.37  2164  axrep4  5054  zfcndrep  9834  bj-alexbiex  33549  bj-alalbial  33551  bj-axrep4  33627  fvineqsneq  34140
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