Theorem ad4antr 712

Description: Deduction adding 4 conjuncts to antecedent. (Contributed by Mario Carneiro, 4-Jan-2017.)

Hypothesis

Ref	Expression
ad2ant.1	⊢ (φ → ψ)

Assertion

Ref	Expression
ad4antr	⊢ (((((φ ∧ χ) ∧ θ) ∧ τ) ∧ η) → ψ)

Proof of Theorem ad4antr

Step	Hyp	Ref	Expression
1		ad2ant.1	. . 3 ⊢ (φ → ψ)
2	1	ad3antrrr 710	. 2 ⊢ ((((φ ∧ χ) ∧ θ) ∧ τ) → ψ)
3	2	adantr 451	1 ⊢ (((((φ ∧ χ) ∧ θ) ∧ τ) ∧ η) → 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:  ad5antr  714