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Mirrors > Home > ILE Home > Th. List > simp2ll | GIF version |
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.) |
Ref | Expression |
---|---|
simp2ll | ⊢ ((𝜃 ∧ ((𝜑 ∧ 𝜓) ∧ 𝜒) ∧ 𝜏) → 𝜑) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simpll 481 | . 2 ⊢ (((𝜑 ∧ 𝜓) ∧ 𝜒) → 𝜑) | |
2 | 1 | 3ad2ant2 926 | 1 ⊢ ((𝜃 ∧ ((𝜑 ∧ 𝜓) ∧ 𝜒) ∧ 𝜏) → 𝜑) |
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: tfrlem5 5930 |
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