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Mirrors > Home > MPE Home > Th. List > simp211 | Structured version Visualization version GIF version |
Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012.) |
Ref | Expression |
---|---|
simp211 | ⊢ ((𝜂 ∧ ((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) ∧ 𝜁) → 𝜑) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simp11 1201 | . 2 ⊢ (((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) → 𝜑) | |
2 | 1 | 3ad2ant2 1132 | 1 ⊢ ((𝜂 ∧ ((𝜑 ∧ 𝜓 ∧ 𝜒) ∧ 𝜃 ∧ 𝜏) ∧ 𝜁) → 𝜑) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ w3a 1085 |
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 396 df-3an 1087 |
This theorem is referenced by: cdleme27a 38308 cdlemk5u 38802 cdlemk6u 38803 cdlemk7u 38811 cdlemk11u 38812 cdlemk12u 38813 cdlemk7u-2N 38829 cdlemk11u-2N 38830 cdlemk12u-2N 38831 cdlemk20-2N 38833 cdlemk22 38834 cdlemk33N 38850 cdlemk53b 38897 cdlemk53 38898 cdlemk55a 38900 cdlemkyyN 38903 cdlemk43N 38904 |
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