Theorem simpr3 963

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

Assertion

Ref	Expression
simpr3	⊢ ((φ ∧ (ψ ∧ χ ∧ θ)) → θ)

Proof of Theorem simpr3

Step	Hyp	Ref	Expression
1		simp3 957	. 2 ⊢ ((ψ ∧ χ ∧ θ) → θ)
2	1	adantl 452	1 ⊢ ((φ ∧ (ψ ∧ χ ∧ θ)) → θ)

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:  simplr3  999  simprr3  1005  simp1r3  1053  simp2r3  1059  simp3r3  1065  3anandis  1283