Metamath Proof Explorer


Theorem frege100

Description: One direction of dffrege99 . Proposition 100 of Frege1879 p. 72. (Contributed by RP, 7-Jul-2020) (Proof modification is discouraged.)

Ref Expression
Hypothesis frege99.z Z U
Assertion frege100 X t+ R I Z ¬ X t+ R Z Z = X

Proof

Step Hyp Ref Expression
1 frege99.z Z U
2 1 dffrege99 ¬ X t+ R Z Z = X X t+ R I Z
3 frege57aid ¬ X t+ R Z Z = X X t+ R I Z X t+ R I Z ¬ X t+ R Z Z = X
4 2 3 ax-mp X t+ R I Z ¬ X t+ R Z Z = X