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Theorem pm2.61d 150
Description: Deduction eliminating an antecedent. (Contributed by NM, 27-Apr-1994.) (Proof shortened by Wolf Lammen, 12-Sep-2013.)
Hypotheses
Ref Expression
pm2.61d.1 (φ → (ψχ))
pm2.61d.2 (φ → (¬ ψχ))
Assertion
Ref Expression
pm2.61d (φχ)

Proof of Theorem pm2.61d
StepHypRef Expression
1 pm2.61d.2 . . . 4 (φ → (¬ ψχ))
21con1d 116 . . 3 (φ → (¬ χψ))
3 pm2.61d.1 . . 3 (φ → (ψχ))
42, 3syld 40 . 2 (φ → (¬ χχ))
54pm2.18d 103 1 (φχ)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem is referenced by:  pm2.61d1  151  pm2.61d2  152  pm5.21ndd  343  bija  344  pm2.61dan  766  ecase3d  909  nfsb4t  2080  pm2.61dne  2593
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