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Mirrors > Home > MPE Home > Th. List > ad4ant124 | Structured version Visualization version GIF version |
Description: Deduction adding conjuncts to antecedent. (Contributed by Alan Sare, 17-Oct-2017.) (Proof shortened by Wolf Lammen, 14-Apr-2022.) |
Ref | Expression |
---|---|
ad4ant3.1 | ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜃) |
Ref | Expression |
---|---|
ad4ant124 | ⊢ ((((𝜑 ∧ 𝜓) ∧ 𝜏) ∧ 𝜒) → 𝜃) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ad4ant3.1 | . . 3 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜃) | |
2 | 1 | 3expa 1119 | . 2 ⊢ (((𝜑 ∧ 𝜓) ∧ 𝜒) → 𝜃) |
3 | 2 | adantlr 714 | 1 ⊢ ((((𝜑 ∧ 𝜓) ∧ 𝜏) ∧ 𝜒) → 𝜃) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 397 ∧ w3a 1088 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 |
This theorem depends on definitions: df-bi 206 df-an 398 df-3an 1090 |
This theorem is referenced by: ad5ant124 1366 ixxin 13341 odf1 19430 m2cpmfo 22258 cnflf 23506 cnfcf 23546 tmdmulg 23596 blin 23927 blsscls2 24013 metcn 24052 xrsxmet 24325 sqf11 26643 dimval 32686 dfgcd3 36205 lindsadd 36481 naddsuc2 42143 hspmbllem2 45343 |
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