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Theorem 19.3 1785
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 1747 . 2 (xφφ)
2 19.3.1 . . 3 xφ
32nfri 1762 . 2 (φxφ)
41, 3impbii 180 1 (xφφ)
Colors of variables: wff setvar class
Syntax hints:  wb 176  wal 1540  wnf 1544
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-11 1746
This theorem depends on definitions:  df-bi 177  df-ex 1542  df-nf 1545
This theorem is referenced by:  19.16  1860  19.17  1861  19.27  1869  19.28  1870  19.37  1873  equsal  1960  2eu4  2287
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