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Mirrors > Home > ILE Home > Th. List > 3ad2antl1 | GIF version |
Description: Deduction adding conjuncts to antecedent. (Contributed by NM, 4-Aug-2007.) |
Ref | Expression |
---|---|
3ad2antl.1 | ⊢ ((𝜑 ∧ 𝜒) → 𝜃) |
Ref | Expression |
---|---|
3ad2antl1 | ⊢ (((𝜑 ∧ 𝜓 ∧ 𝜏) ∧ 𝜒) → 𝜃) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 3ad2antl.1 | . . 3 ⊢ ((𝜑 ∧ 𝜒) → 𝜃) | |
2 | 1 | adantlr 446 | . 2 ⊢ (((𝜑 ∧ 𝜏) ∧ 𝜒) → 𝜃) |
3 | 2 | 3adantl2 1061 | 1 ⊢ (((𝜑 ∧ 𝜓 ∧ 𝜏) ∧ 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: acexmid 5511 ordiso2 6357 addlocpr 6634 distrlem1prl 6680 distrlem1pru 6681 ltsopr 6694 addcanprlemu 6713 fzo1fzo0n0 9039 expival 9257 |
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