Theorem 3adantr2 1115

Description: Deduction adding a conjunct to antecedent. (Contributed by NM, 27-Apr-2005.)

Hypothesis

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

Assertion

Ref	Expression
3adantr2	⊢ ((φ ∧ (ψ ∧ τ ∧ χ)) → θ)

Proof of Theorem 3adantr2

Step	Hyp	Ref	Expression
1		3simpb 953	. 2 ⊢ ((ψ ∧ τ ∧ χ) → (ψ ∧ χ))
2		3adantr.1	. 2 ⊢ ((φ ∧ (ψ ∧ χ)) → θ)
3	1, 2	sylan2 460	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:  3adant3r2  1161