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Theorem nfimOLD 1814
 Description: If x is not free in φ and ψ, it is not free in (φ → ψ). (Contributed by Mario Carneiro, 11-Aug-2016.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
nfim.1 xφ
nfim.2 xψ
Assertion
Ref Expression
nfimOLD x(φψ)

Proof of Theorem nfimOLD
StepHypRef Expression
1 nfim.1 . . . 4 xφ
21a1i 10 . . 3 ( ⊤ → Ⅎxφ)
3 nfim.2 . . . 4 xψ
43a1i 10 . . 3 ( ⊤ → Ⅎxψ)
52, 4nfimd 1808 . 2 ( ⊤ → Ⅎx(φψ))
65trud 1323 1 x(φψ)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ⊤ wtru 1316  Ⅎwnf 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-6 1729  ax-11 1746 This theorem depends on definitions:  df-bi 177  df-tru 1319  df-ex 1542  df-nf 1545 This theorem is referenced by: (None)
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