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Mirrors > Home > MPE Home > Th. List > adantrrl | Structured version Visualization version GIF version |
Description: Deduction adding a conjunct to antecedent. (Contributed by NM, 26-Dec-2004.) (Proof shortened by Wolf Lammen, 4-Dec-2012.) |
Ref | Expression |
---|---|
adantr2.1 | ⊢ ((𝜑 ∧ (𝜓 ∧ 𝜒)) → 𝜃) |
Ref | Expression |
---|---|
adantrrl | ⊢ ((𝜑 ∧ (𝜓 ∧ (𝜏 ∧ 𝜒))) → 𝜃) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simpr 477 | . 2 ⊢ ((𝜏 ∧ 𝜒) → 𝜒) | |
2 | adantr2.1 | . 2 ⊢ ((𝜑 ∧ (𝜓 ∧ 𝜒)) → 𝜃) | |
3 | 1, 2 | sylanr2 670 | 1 ⊢ ((𝜑 ∧ (𝜓 ∧ (𝜏 ∧ 𝜒))) → 𝜃) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 387 |
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 199 df-an 388 |
This theorem is referenced by: zorn2lem6 9713 ltmul12a 11289 mndind 17824 neiint 21406 neissex 21429 1stcfb 21747 1stcrest 21755 grporcan 28062 mdslmd3i 29880 colineardim1 32983 cvratlem 35950 ps-2 36007 |
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