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Mirrors > Home > MPE Home > Th. List > Mathboxes > frege10 | Structured version Visualization version GIF version |
Description: Result commuting antecedents within an antecedent. Proposition 10 of [Frege1879] p. 36. (Contributed by RP, 24-Dec-2019.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
frege10 | ⊢ (((𝜑 → (𝜓 → 𝜒)) → 𝜃) → ((𝜓 → (𝜑 → 𝜒)) → 𝜃)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax-frege8 42169 | . 2 ⊢ ((𝜓 → (𝜑 → 𝜒)) → (𝜑 → (𝜓 → 𝜒))) | |
2 | frege9 42172 | . 2 ⊢ (((𝜓 → (𝜑 → 𝜒)) → (𝜑 → (𝜓 → 𝜒))) → (((𝜑 → (𝜓 → 𝜒)) → 𝜃) → ((𝜓 → (𝜑 → 𝜒)) → 𝜃))) | |
3 | 1, 2 | ax-mp 5 | 1 ⊢ (((𝜑 → (𝜓 → 𝜒)) → 𝜃) → ((𝜓 → (𝜑 → 𝜒)) → 𝜃)) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 |
This theorem was proved from axioms: ax-mp 5 ax-frege1 42150 ax-frege2 42151 ax-frege8 42169 |
This theorem is referenced by: frege30 42192 |
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