Metamath Proof Explorer


Theorem frege101

Description: Lemma for frege102 . Proposition 101 of Frege1879 p. 72. (Contributed by RP, 7-Jul-2020) (Proof modification is discouraged.)

Ref Expression
Hypothesis frege99.z Z U
Assertion frege101 Z = X Z R V X t+ R V X t+ R Z Z R V X t+ R V X t+ R I Z Z R V X t+ R V

Proof

Step Hyp Ref Expression
1 frege99.z Z U
2 1 frege100 X t+ R I Z ¬ X t+ R Z Z = X
3 frege48 X t+ R I Z ¬ X t+ R Z Z = X Z = X Z R V X t+ R V X t+ R Z Z R V X t+ R V X t+ R I Z Z R V X t+ R V
4 2 3 ax-mp Z = X Z R V X t+ R V X t+ R Z Z R V X t+ R V X t+ R I Z Z R V X t+ R V