Theorem 3adantr3 1116

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
3adantr3	⊢ ((φ ∧ (ψ ∧ χ ∧ τ)) → θ)

Proof of Theorem 3adantr3

Step	Hyp	Ref	Expression
1		3simpa 952	. 2 ⊢ ((ψ ∧ χ ∧ τ) → (ψ ∧ χ))
2		3adantr.1	. 2 ⊢ ((φ ∧ (ψ ∧ χ)) → θ)
3	1, 2	sylan2 460	1 ⊢ ((φ ∧ (ψ ∧ χ ∧ τ)) → 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:  3ad2antr1  1120  3ad2antr2  1121  3adant3r3  1162