Theorem simpl1 958

Description: Simplification rule. (Contributed by Jeff Hankins, 17-Nov-2009.)

Assertion

Ref	Expression
simpl1	⊢ (((φ ∧ ψ ∧ χ) ∧ θ) → φ)

Proof of Theorem simpl1

Step	Hyp	Ref	Expression
1		simp1 955	. 2 ⊢ ((φ ∧ ψ ∧ χ) → φ)
2	1	adantr 451	1 ⊢ (((φ ∧ ψ ∧ χ) ∧ θ) → φ)

Syntax hints:   → wi 4   ∧ wa 358   ∧ w3a 934

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 177  df-an 360  df-3an 936

This theorem is referenced by:  simpll1  994  simprl1  1000  simp1l1  1048  simp2l1  1054  simp3l1  1060  3anandirs  1284  rspc3ev  2966  nnsucelr  4429  tfinltfin  4502  sfindbl  4531  enadjlem1  6060  enadj  6061  enprmaplem5  6081  lemuc2  6255  lecadd2  6267