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Theorem 19.21h 1797
Description: Theorem 19.21 of [Margaris] p. 90. The hypothesis can be thought of as "x is not free in φ." (Contributed by NM, 1-Aug-2017.) (Proof shortened by Wolf Lammen, 1-Jan-2018.)
Hypothesis
Ref Expression
19.21h.1 (φxφ)
Assertion
Ref Expression
19.21h (x(φψ) ↔ (φxψ))

Proof of Theorem 19.21h
StepHypRef Expression
1 19.21h.1 . . 3 (φxφ)
21nfi 1551 . 2 xφ
3219.21 1796 1 (x(φψ) ↔ (φxψ))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 176  wal 1540
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-6 1729  ax-11 1746
This theorem depends on definitions:  df-bi 177  df-ex 1542  df-nf 1545
This theorem is referenced by:  hbim1  1810  ax12olem6  1932
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