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Mirrors > Home > MPE Home > Th. List > pm3.33 | Structured version Visualization version GIF version |
Description: Theorem *3.33 (Syll) of [WhiteheadRussell] p. 112. (Contributed by NM, 3-Jan-2005.) |
Ref | Expression |
---|---|
pm3.33 | ⊢ (((𝜑 → 𝜓) ∧ (𝜓 → 𝜒)) → (𝜑 → 𝜒)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | imim1 81 | . 2 ⊢ ((𝜑 → 𝜓) → ((𝜓 → 𝜒) → (𝜑 → 𝜒))) | |
2 | 1 | imp 444 | 1 ⊢ (((𝜑 → 𝜓) ∧ (𝜓 → 𝜒)) → (𝜑 → 𝜒)) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 383 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 |
This theorem depends on definitions: df-bi 196 df-an 385 |
This theorem is referenced by: alsyl 1811 ucncn 21899 bnj1023 30105 bnj907 30289 2sb5ndALT 38190 |
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