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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 1152 | 1 ⊢ ((𝜒 ∧ 𝜃 ∧ 𝜑) → (𝜒 ∧ 𝜃 ∧ 𝜓)) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ w3a 1088 |
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 206 df-an 398 df-3an 1090 |
This theorem is referenced by: syl3an3 1166 syl3anl3 1415 syl3anr3 1419 elioo4g 13333 ssnn0fi 13899 tmdcn2 23463 axcont 27974 numclwwlk3 29378 minvecolem3 29867 bnj556 33576 bnj557 33577 bnj1145 33669 btwnconn1lem4 34728 btwnconn1lem5 34729 btwnconn1lem6 34730 bj-ceqsalt 35406 bj-ceqsaltv 35407 |
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