Theorem 3simpb 592

Description: Simplification of triple conjunction.

Assertion

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

Proof of Theorem 3simpb

Step	Hyp	Ref	Expression
1		3ancomb 589	. 2 ⊢ ((φ ∧ ψ ∧ χ) ↔ (φ ∧ χ ∧ ψ))
2		3simpa 591	. 2 ⊢ ((φ ∧ χ ∧ ψ) → (φ ∧ χ))
3	1, 2	sylbi 174	1 ⊢ ((φ ∧ ψ ∧ χ) → (φ ∧ χ))

Syntax hints:   → wi 2   ∧ wa 196   ∧ w3a 581

This theorem is referenced by:  3adant2 598  po3nr 2136

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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