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Theorem 19.3 1428
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 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 1382 . 2 (xφφ)
2 19.3.1 . . 3 xφ
32nfri 1393 . 2 (φxφ)
41, 3impbii 117 1 (xφφ)
Colors of variables: wff set class
Syntax hints:  wb 98  wal 1226  wnf 1329
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-4 1381
This theorem depends on definitions:  df-bi 110  df-nf 1330
This theorem is referenced by:  19.16  1429  19.17  1430  19.27  1435  19.28  1437  19.37-1  1546  rexxfrd  4145
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