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Mirrors > Home > MPE Home > Th. List > adantrd | Structured version Visualization version GIF version |
Description: Deduction adding a conjunct to the right of an antecedent. (Contributed by NM, 4-May-1994.) |
Ref | Expression |
---|---|
adantrd.1 | ⊢ (𝜑 → (𝜓 → 𝜒)) |
Ref | Expression |
---|---|
adantrd | ⊢ (𝜑 → ((𝜓 ∧ 𝜃) → 𝜒)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simpl 486 | . 2 ⊢ ((𝜓 ∧ 𝜃) → 𝜓) | |
2 | adantrd.1 | . 2 ⊢ (𝜑 → (𝜓 → 𝜒)) | |
3 | 1, 2 | syl5 34 | 1 ⊢ (𝜑 → ((𝜓 ∧ 𝜃) → 𝜒)) |
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