Theorem 3adantl2 1112

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
3adantl2	⊢ (((φ ∧ τ ∧ ψ) ∧ χ) → θ)

Proof of Theorem 3adantl2

Step	Hyp	Ref	Expression
1		3simpb 953	. 2 ⊢ ((φ ∧ τ ∧ ψ) → (φ ∧ ψ))
2		3adantl.1	. 2 ⊢ (((φ ∧ ψ) ∧ χ) → θ)
3	1, 2	sylan 457	1 ⊢ (((φ ∧ τ ∧ ψ) ∧ χ) → θ)

This proof depends on syntax axioms:   → wi 4   ∧ wa 358   ∧ w3a 934

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

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

This theorem is used by:  3ad2antl1  1117