Theorem 3ad2antl1 1117

Description: Deduction adding conjuncts to antecedent. (Contributed by NM, 4-Aug-2007.)

Hypothesis

Ref	Expression
3ad2antl.1	⊢ ((φ ∧ χ) → θ)

Assertion

Ref	Expression
3ad2antl1	⊢ (((φ ∧ ψ ∧ τ) ∧ χ) → θ)

Proof of Theorem 3ad2antl1

Step	Hyp	Ref	Expression
1		3ad2antl.1	. . 3 ⊢ ((φ ∧ χ) → θ)
2	1	adantlr 695	. 2 ⊢ (((φ ∧ τ) ∧ χ) → θ)
3	2	3adantl2 1112	1 ⊢ (((φ ∧ ψ ∧ τ) ∧ 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:  sfintfin  4533  ce2le  6234