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Theorem nfbiOLD 1835
 Description: If x is not free in φ and ψ, it is not free in (φ ↔ ψ). (Contributed by Mario Carneiro, 11-Aug-2016.) (New usage is discouraged.)
Hypotheses
Ref Expression
nf.1 xφ
nf.2 xψ
Assertion
Ref Expression
nfbiOLD x(φψ)

Proof of Theorem nfbiOLD
StepHypRef Expression
1 dfbi2 609 . 2 ((φψ) ↔ ((φψ) (ψφ)))
2 nf.1 . . . 4 xφ
3 nf.2 . . . 4 xψ
42, 3nfim 1813 . . 3 x(φψ)
53, 2nfim 1813 . . 3 x(ψφ)
64, 5nfan 1824 . 2 x((φψ) (ψφ))
71, 6nfxfr 1570 1 x(φψ)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ↔ wb 176   ∧ wa 358  Ⅎwnf 1544 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 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-an 360  df-tru 1319  df-ex 1542  df-nf 1545 This theorem is referenced by: (None)
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