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Theorem pm2.61ian 765
Description: Elimination of an antecedent. (Contributed by NM, 1-Jan-2005.)
Hypotheses
Ref Expression
pm2.61ian.1 ((φ ψ) → χ)
pm2.61ian.2 ((¬ φ ψ) → χ)
Assertion
Ref Expression
pm2.61ian (ψχ)

Proof of Theorem pm2.61ian
StepHypRef Expression
1 pm2.61ian.1 . . 3 ((φ ψ) → χ)
21ex 423 . 2 (φ → (ψχ))
3 pm2.61ian.2 . . 3 ((¬ φ ψ) → χ)
43ex 423 . 2 φ → (ψχ))
52, 4pm2.61i 156 1 (ψχ)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4   wa 358
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 177  df-an 360
This theorem is referenced by:  4cases  915  consensus  925  sbcom  2089  ax11indalem  2197  phi11lem1  4595  xpcan2  5058
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