Theorem simpr2 962

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

Assertion

Ref	Expression
simpr2	⊢ ((φ ∧ (ψ ∧ χ ∧ θ)) → χ)

Proof of Theorem simpr2

Step	Hyp	Ref	Expression
1		simp2 956	. 2 ⊢ ((ψ ∧ χ ∧ θ) → χ)
2	1	adantl 452	1 ⊢ ((φ ∧ (ψ ∧ χ ∧ θ)) → χ)

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:  simplr2  998  simprr2  1004  simp1r2  1052  simp2r2  1058  simp3r2  1064  3anandis  1283