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Mirrors > Home > MPE Home > Th. List > Mathboxes > frege55a | Structured version Visualization version GIF version |
Description: Proposition 55 of [Frege1879] p. 50. (Contributed by RP, 24-Dec-2019.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
frege55a | ⊢ ((𝜑 ↔ 𝜓) → if-(𝜓, 𝜑, ¬ 𝜑)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | frege54cor1a 37178 | . 2 ⊢ if-(𝜑, 𝜑, ¬ 𝜑) | |
2 | frege53a 37174 | . 2 ⊢ (if-(𝜑, 𝜑, ¬ 𝜑) → ((𝜑 ↔ 𝜓) → if-(𝜓, 𝜑, ¬ 𝜑))) | |
3 | 1, 2 | ax-mp 5 | 1 ⊢ ((𝜑 ↔ 𝜓) → if-(𝜓, 𝜑, ¬ 𝜑)) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 → wi 4 ↔ wb 195 if-wif 1006 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-frege8 37123 ax-frege28 37144 ax-frege52a 37171 ax-frege54a 37176 |
This theorem depends on definitions: df-bi 196 df-or 384 df-an 385 df-ifp 1007 |
This theorem is referenced by: frege55cor1a 37183 |
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