Metamath Proof Explorer


Theorem tradd

Description: Add top ad a conjunct. (Contributed by Giovanni Mascellani, 24-May-2019)

Ref Expression
Hypothesis tradd.1 ⊢ φ ↔ ψ
Assertion tradd ⊢ φ ↔ ⊤ ∧ ψ

Proof

Step Hyp Ref Expression
1 tradd.1 ⊢ φ ↔ ψ
2 truan ⊢ ⊤ ∧ ψ ↔ ψ
3 1 2 bitr4i ⊢ φ ↔ ⊤ ∧ ψ