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Mirrors > Home > MPE Home > Th. List > pm3.4 | Structured version Visualization version GIF version |
Description: Conjunction implies implication. Theorem *3.4 of [WhiteheadRussell] p. 113. (Contributed by NM, 31-Jul-1995.) |
Ref | Expression |
---|---|
pm3.4 | ⊢ ((𝜑 ∧ 𝜓) → (𝜑 → 𝜓)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simpr 488 | . 2 ⊢ ((𝜑 ∧ 𝜓) → 𝜓) | |
2 | 1 | a1d 25 | 1 ⊢ ((𝜑 ∧ 𝜓) → (𝜑 → 𝜓)) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 399 |
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 210 df-an 400 |
This theorem is referenced by: cases2ALT 1048 bj-animbi 34377 bj-sbsb 34651 jabtaib 43966 confun4 43976 plvcofphax 43981 afvres 44197 |
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