Theorem 3simpa 591

Description: Simplification of triple conjunction.

Assertion

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

Proof of Theorem 3simpa

Step	Hyp	Ref	Expression
1		df-3an 583	. 2 ⊢ ((φ ∧ ψ ∧ χ) ↔ ((φ ∧ ψ) ∧ χ))
2	1	pm3.26bd 259	1 ⊢ ((φ ∧ ψ ∧ χ) → (φ ∧ ψ))

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

This theorem is referenced by:  3simpb 592  3simpc 593  3simp1 594  3simp2 595  3adant3 599  dfwe2 2187  oaord 3149  nnmord 3189  divdiv23t 4271  strlem3a 5693

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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