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Mirrors > Home > MPE Home > Th. List > pm3.43 | Structured version Visualization version GIF version |
Description: Theorem *3.43 (Comp) of [WhiteheadRussell] p. 113. (Contributed by NM, 3-Jan-2005.) |
Ref | Expression |
---|---|
pm3.43 | ⊢ (((𝜑 → 𝜓) ∧ (𝜑 → 𝜒)) → (𝜑 → (𝜓 ∧ 𝜒))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pm3.43i 476 | . 2 ⊢ ((𝜑 → 𝜓) → ((𝜑 → 𝜒) → (𝜑 → (𝜓 ∧ 𝜒)))) | |
2 | 1 | imp 410 | 1 ⊢ (((𝜑 → 𝜓) ∧ (𝜑 → 𝜒)) → (𝜑 → (𝜓 ∧ 𝜒))) |
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: jcab 521 anim12ii 621 darapti 2684 eqvincg 3555 bnj1110 32675 jm2.18 40513 jm2.15nn0 40528 jm2.16nn0 40529 cotrintab 40898 |
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