Metamath Proof Explorer


Theorem ad4antr

Description: Deduction adding 4 conjuncts to antecedent. (Contributed by Mario Carneiro, 4-Jan-2017) (Proof shortened by Wolf Lammen, 5-Apr-2022)

Ref Expression
Hypothesis ad2ant.1 φ ψ
Assertion ad4antr φ χ θ τ η ψ

Proof

Step Hyp Ref Expression
1 ad2ant.1 φ ψ
2 1 adantr φ χ ψ
3 2 ad3antrrr φ χ θ τ η ψ