![]() |
Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > ILE Home > Th. List > 3ad2antl2 | GIF version |
Description: Deduction adding conjuncts to antecedent. (Contributed by NM, 4-Aug-2007.) |
Ref | Expression |
---|---|
3ad2antl.1 | ⊢ ((𝜑 ∧ 𝜒) → 𝜃) |
Ref | Expression |
---|---|
3ad2antl2 | ⊢ (((𝜓 ∧ 𝜑 ∧ 𝜏) ∧ 𝜒) → 𝜃) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 3ad2antl.1 | . . 3 ⊢ ((𝜑 ∧ 𝜒) → 𝜃) | |
2 | 1 | adantlr 477 | . 2 ⊢ (((𝜑 ∧ 𝜏) ∧ 𝜒) → 𝜃) |
3 | 2 | 3adantl1 1153 | 1 ⊢ (((𝜓 ∧ 𝜑 ∧ 𝜏) ∧ 𝜒) → 𝜃) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∧ wa 104 ∧ w3a 978 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 |
This theorem depends on definitions: df-bi 117 df-3an 980 |
This theorem is referenced by: fcofo 5784 cocan1 5787 acexmid 5873 caovimo 6067 ordiso2 7033 mkvprop 7155 ltpopr 7593 ltsopr 7594 addcanprleml 7612 addcanprlemu 7613 aptiprlemu 7638 dvdsmodexp 11797 muldvds1 11818 lcmdvds 12073 cnpnei 13650 |
Copyright terms: Public domain | W3C validator |