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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 391 | 1 ⊢ (𝜑 ↔ (𝜑 ∧ 𝜑)) |
Colors of variables: wff set class |
Syntax hints: ∧ wa 104 ↔ wb 105 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 |
This theorem depends on definitions: df-bi 117 |
This theorem is referenced by: anidm 396 anabsan 575 sbidm 1851 euind 2924 reuind 2942 xrmaxiflemcom 11228 srg1zr 12983 crngunit 13092 |
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