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Mirrors > Home > MPE Home > Th. List > adantrlr | 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 |
---|---|
adantrlr | ⊢ ((𝜑 ∧ ((𝜓 ∧ 𝜏) ∧ 𝜒)) → 𝜃) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simpl 483 | . 2 ⊢ ((𝜓 ∧ 𝜏) → 𝜓) | |
2 | adantr2.1 | . 2 ⊢ ((𝜑 ∧ (𝜓 ∧ 𝜒)) → 𝜃) | |
3 | 1, 2 | sylanr1 680 | 1 ⊢ ((𝜑 ∧ ((𝜓 ∧ 𝜏) ∧ 𝜒)) → 𝜃) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 396 |
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 397 |
This theorem is referenced by: smoord 8367 addsrmo 11070 mulsrmo 11071 lediv12a 12109 nrmmetd 24090 pntrmax 27074 ablo4 29841 mdslmd3i 31623 atom1d 31644 fsumiunle 32073 esumiun 33161 poimirlem28 36602 fdc 36699 incsequz 36702 crngm4 36957 ps-2 38435 aacllem 47926 |
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