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Mirrors > Home > ILE Home > Th. List > pm4.24 | GIF version |
Description: Theorem *4.24 of [WhiteheadRussell] p. 117. (Contributed by NM, 3-Jan-2005.) (Revised by NM, 14-Mar-2014.) |
Ref | Expression |
---|---|
pm4.24 | ⊢ (φ ↔ (φ ∧ φ)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | id 19 | . 2 ⊢ (φ → φ) | |
2 | 1 | pm4.71i 371 | 1 ⊢ (φ ↔ (φ ∧ φ)) |
Colors of variables: wff set class |
Syntax hints: ∧ wa 97 ↔ wb 98 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 |
This theorem depends on definitions: df-bi 110 |
This theorem is referenced by: anidm 376 anabsan 509 sbidm 1728 euind 2722 reuind 2738 |
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