Theorem ad7antr 718

Description: Deduction adding 7 conjuncts to antecedent. (Contributed by Mario Carneiro, 4-Jan-2017.)

Hypothesis

Ref	Expression
ad2ant.1	⊢ (φ → ψ)

Assertion

Ref	Expression
ad7antr	⊢ ((((((((φ ∧ χ) ∧ θ) ∧ τ) ∧ η) ∧ ζ) ∧ σ) ∧ ρ) → ψ)

Proof of Theorem ad7antr

Step	Hyp	Ref	Expression
1		ad2ant.1	. . 3 ⊢ (φ → ψ)
2	1	ad6antr 716	. 2 ⊢ (((((((φ ∧ χ) ∧ θ) ∧ τ) ∧ η) ∧ ζ) ∧ σ) → ψ)
3	2	adantr 451	1 ⊢ ((((((((φ ∧ χ) ∧ θ) ∧ τ) ∧ η) ∧ ζ) ∧ σ) ∧ ρ) → ψ)

Syntax hints:   → wi 4   ∧ wa 358

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

This theorem is referenced by:  ad8antr  720