Theorem 3adantl3 1113

Description: Deduction adding a conjunct to antecedent. (Contributed by NM, 24-Feb-2005.)

Hypothesis

Ref	Expression
3adantl.1	⊢ (((φ ∧ ψ) ∧ χ) → θ)

Assertion

Ref	Expression
3adantl3	⊢ (((φ ∧ ψ ∧ τ) ∧ χ) → θ)

Proof of Theorem 3adantl3

Step	Hyp	Ref	Expression
1		3simpa 952	. 2 ⊢ ((φ ∧ ψ ∧ τ) → (φ ∧ ψ))
2		3adantl.1	. 2 ⊢ (((φ ∧ ψ) ∧ χ) → θ)
3	1, 2	sylan 457	1 ⊢ (((φ ∧ ψ ∧ τ) ∧ χ) → 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: (None)