Theorem 3simp1 594

Description: Simplification of triple conjunction.

Assertion

Ref	Expression
3simp1	⊢ ((φ ∧ ψ ∧ χ) → φ)

Proof of Theorem 3simp1

Step	Hyp	Ref	Expression
1		3simpa 591	. 2 ⊢ ((φ ∧ ψ ∧ χ) → (φ ∧ ψ))
2	1	pm3.26d 258	1 ⊢ ((φ ∧ ψ ∧ χ) → φ)

Syntax hints:   → wi 2   ∧ w3a 581

This theorem is referenced by:  limord 2283  nlimsuc 2363  find 2396  divdiv23t 4271  ltdivmult 4408  nnleltp1t 4448  suprub 4513  sqrlem20 4750  shlej1t 5356  atexch 5769  atcvatlem 5770

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6

This theorem depends on definitions:  df-bi 128  df-an 198  df-3an 583

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