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Mirrors > Home > ILE Home > Th. List > 3anim1i | GIF version |
Description: Add two conjuncts to antecedent and consequent. (Contributed by Jeff Hankins, 16-Aug-2009.) |
Ref | Expression |
---|---|
3animi.1 | ⊢ (𝜑 → 𝜓) |
Ref | Expression |
---|---|
3anim1i | ⊢ ((𝜑 ∧ 𝜒 ∧ 𝜃) → (𝜓 ∧ 𝜒 ∧ 𝜃)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 3animi.1 | . 2 ⊢ (𝜑 → 𝜓) | |
2 | id 19 | . 2 ⊢ (𝜒 → 𝜒) | |
3 | id 19 | . 2 ⊢ (𝜃 → 𝜃) | |
4 | 1, 2, 3 | 3anim123i 1123 | 1 ⊢ ((𝜑 ∧ 𝜒 ∧ 𝜃) → (𝜓 ∧ 𝜒 ∧ 𝜃)) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∧ w3a 919 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 |
This theorem depends on definitions: df-bi 115 df-3an 921 |
This theorem is referenced by: syl3an1 1202 syl3anl1 1217 syl3anr1 1221 elioc2 8959 elico2 8960 elicc2 8961 dvdsleabs2 10246 |
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