Theorem 3simp3 596

Description: Simplification of triple conjunction.

Assertion

Ref	Expression
3simp3	⊢ ((φ ∧ ψ ∧ χ) → χ)

Proof of Theorem 3simp3

Step	Hyp	Ref	Expression
1		3simpc 593	. 2 ⊢ ((φ ∧ ψ ∧ χ) → (ψ ∧ χ))
2	1	pm3.27d 262	1 ⊢ ((φ ∧ ψ ∧ χ) → χ)

Syntax hints:   → wi 2   ∧ w3a 581

This theorem is referenced by:  limuni 2284  fiint 3445  ltsopi 3810  addsubasst 4150  divdiv23t 4271  sqrlem20 4750  shlej1t 5356  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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