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Mirrors > Home > NFE Home > Th. List > simp1l | GIF version |
Description: Simplification of triple conjunction. (Contributed by NM, 9-Nov-2011.) |
Ref | Expression |
---|---|
simp1l | ⊢ (((φ ∧ ψ) ∧ χ ∧ θ) → φ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simpl 443 | . 2 ⊢ ((φ ∧ ψ) → φ) | |
2 | 1 | 3ad2ant1 976 | 1 ⊢ (((φ ∧ ψ) ∧ χ ∧ θ) → φ) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∧ wa 358 ∧ w3a 934 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-3 7 ax-mp 8 |
This theorem depends on definitions: df-bi 177 df-an 360 df-3an 936 |
This theorem is referenced by: simpl1l 1006 simpr1l 1012 simp11l 1066 simp21l 1072 simp31l 1078 ncfindi 4475 tfinpw1 4494 tfinltfinlem1 4500 nnpweq 4523 sfintfin 4532 sfinltfin 4535 |
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