Metamath Proof Explorer


Theorem frege11

Description: Elimination of a nested antecedent as a partial converse of ja . If the proposition that ps takes place or ph does not is a sufficient condition for ch , then ps by itself is a sufficient condition for ch . Identical to jarr . Proposition 11 of Frege1879 p. 36. (Contributed by RP, 24-Dec-2019) (Proof modification is discouraged.)

Ref Expression
Assertion frege11 φ ψ χ ψ χ

Proof

Step Hyp Ref Expression
1 ax-frege1 ψ φ ψ
2 frege9 ψ φ ψ φ ψ χ ψ χ
3 1 2 ax-mp φ ψ χ ψ χ