Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > 3adantl2 | GIF version |
Description: Deduction adding a conjunct to antecedent. (Contributed by NM, 24-Feb-2005.) |
Ref | Expression |
---|---|
3adantl.1 | ⊢ (((𝜑 ∧ 𝜓) ∧ 𝜒) → 𝜃) |
Ref | Expression |
---|---|
3adantl2 | ⊢ (((𝜑 ∧ 𝜏 ∧ 𝜓) ∧ 𝜒) → 𝜃) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 3simpb 902 | . 2 ⊢ ((𝜑 ∧ 𝜏 ∧ 𝜓) → (𝜑 ∧ 𝜓)) | |
2 | 3adantl.1 | . 2 ⊢ (((𝜑 ∧ 𝜓) ∧ 𝜒) → 𝜃) | |
3 | 1, 2 | sylan 267 | 1 ⊢ (((𝜑 ∧ 𝜏 ∧ 𝜓) ∧ 𝜒) → 𝜃) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∧ wa 97 ∧ w3a 885 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 |
This theorem depends on definitions: df-bi 110 df-3an 887 |
This theorem is referenced by: 3ad2antl1 1066 nnmord 6090 ltaprg 6717 lediv2a 7861 zdiv 8328 |
Copyright terms: Public domain | W3C validator |