Theorem ad3antrrr 710

Description: Deduction adding three conjuncts to antecedent. (Contributed by NM, 28-Jul-2012.)

Hypothesis

Ref	Expression
ad2ant.1	⊢ (φ → ψ)

Assertion

Ref	Expression
ad3antrrr	⊢ ((((φ ∧ χ) ∧ θ) ∧ τ) → ψ)

Proof of Theorem ad3antrrr

Step	Hyp	Ref	Expression
1		ad2ant.1	. . 3 ⊢ (φ → ψ)
2	1	adantr 451	. 2 ⊢ ((φ ∧ χ) → ψ)
3	2	ad2antrr 706	1 ⊢ ((((φ ∧ χ) ∧ θ) ∧ τ) → ψ)

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

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

This theorem is used by:  ad4antr  712  ncfinraise  4482