Theorem simpr1 961

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

Assertion

Ref	Expression
simpr1	⊢ ((φ ∧ (ψ ∧ χ ∧ θ)) → ψ)

Proof of Theorem simpr1

Step	Hyp	Ref	Expression
1		simp1 955	. 2 ⊢ ((ψ ∧ χ ∧ θ) → ψ)
2	1	adantl 452	1 ⊢ ((φ ∧ (ψ ∧ χ ∧ θ)) → ψ)

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:  simplr1  997  simprr1  1003  simp1r1  1051  simp2r1  1057  simp3r1  1063  3anandis  1283  sfinltfin  4536  enadj  6061