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Mirrors > Home > ILE Home > Th. List > simp3ll | GIF version |
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.) |
Ref | Expression |
---|---|
simp3ll | ⊢ ((𝜃 ∧ 𝜏 ∧ ((𝜑 ∧ 𝜓) ∧ 𝜒)) → 𝜑) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simpll 519 | . 2 ⊢ (((𝜑 ∧ 𝜓) ∧ 𝜒) → 𝜑) | |
2 | 1 | 3ad2ant3 1009 | 1 ⊢ ((𝜃 ∧ 𝜏 ∧ ((𝜑 ∧ 𝜓) ∧ 𝜒)) → 𝜑) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ∧ wa 103 ∧ w3a 967 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 |
This theorem depends on definitions: df-bi 116 df-3an 969 |
This theorem is referenced by: f1oiso2 5792 prarloc 7438 tgqioo 13145 |
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