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Mirrors > Home > ILE Home > Th. List > pm5.5 | GIF version |
Description: Theorem *5.5 of [WhiteheadRussell] p. 125. (Contributed by NM, 3-Jan-2005.) |
Ref | Expression |
---|---|
pm5.5 | ⊢ (𝜑 → ((𝜑 → 𝜓) ↔ 𝜓)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | biimt 241 | . 2 ⊢ (𝜑 → (𝜓 ↔ (𝜑 → 𝜓))) | |
2 | 1 | bicomd 141 | 1 ⊢ (𝜑 → ((𝜑 → 𝜓) ↔ 𝜓)) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ↔ 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: imim21b 253 nfabdw 2338 elabgt 2878 sbceqal 3018 dffun8 5239 ordiso2 7027 indstr2 9585 dfgcd2 11985 |
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