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Mirrors > Home > MPE Home > Th. List > adantl3r | Structured version Visualization version GIF version |
Description: Deduction adding 1 conjunct to antecedent. (Contributed by Thierry Arnoux, 11-Feb-2018.) |
Ref | Expression |
---|---|
adantl3r.1 | ⊢ ((((𝜑 ∧ 𝜌) ∧ 𝜇) ∧ 𝜆) → 𝜅) |
Ref | Expression |
---|---|
adantl3r | ⊢ (((((𝜑 ∧ 𝜎) ∧ 𝜌) ∧ 𝜇) ∧ 𝜆) → 𝜅) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | adantl3r.1 | . . . 4 ⊢ ((((𝜑 ∧ 𝜌) ∧ 𝜇) ∧ 𝜆) → 𝜅) | |
2 | 1 | ex 449 | . . 3 ⊢ (((𝜑 ∧ 𝜌) ∧ 𝜇) → (𝜆 → 𝜅)) |
3 | 2 | adantllr 751 | . 2 ⊢ ((((𝜑 ∧ 𝜎) ∧ 𝜌) ∧ 𝜇) → (𝜆 → 𝜅)) |
4 | 3 | imp 444 | 1 ⊢ (((((𝜑 ∧ 𝜎) ∧ 𝜌) ∧ 𝜇) ∧ 𝜆) → 𝜅) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 383 |
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 196 df-an 385 |
This theorem is referenced by: adantl4r 783 ad5ant1345 1308 iscgrglt 25209 legov 25280 dfcgra2 25521 omssubadd 29689 poimirlem29 32608 adantlllr 38222 hspmbllem2 39517 |
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