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Mirrors > Home > MPE Home > Th. List > 3anim3i | Structured version Visualization version GIF version |
Description: Add two conjuncts to antecedent and consequent. (Contributed by Jeff Hankins, 19-Aug-2009.) |
Ref | Expression |
---|---|
3animi.1 | ⊢ (𝜑 → 𝜓) |
Ref | Expression |
---|---|
3anim3i | ⊢ ((𝜒 ∧ 𝜃 ∧ 𝜑) → (𝜒 ∧ 𝜃 ∧ 𝜓)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | id 22 | . 2 ⊢ (𝜒 → 𝜒) | |
2 | id 22 | . 2 ⊢ (𝜃 → 𝜃) | |
3 | 3animi.1 | . 2 ⊢ (𝜑 → 𝜓) | |
4 | 1, 2, 3 | 3anim123i 1153 | 1 ⊢ ((𝜒 ∧ 𝜃 ∧ 𝜑) → (𝜒 ∧ 𝜃 ∧ 𝜓)) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ w3a 1089 |
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 df-3an 1091 |
This theorem is referenced by: syl3an3 1167 syl3anl3 1416 syl3anr3 1420 elioo4g 12960 ssnn0fi 13523 tmdcn2 22940 axcont 27021 numclwwlk3 28422 minvecolem3 28911 bnj556 32547 bnj557 32548 bnj1145 32640 btwnconn1lem4 34078 btwnconn1lem5 34079 btwnconn1lem6 34080 bj-ceqsalt 34758 bj-ceqsaltv 34759 |
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