Theorem tradd 36190

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

Hypothesis

Ref	Expression
tradd.1	⊢ (𝜑 ↔ 𝜓)

Assertion

Ref	Expression
tradd	⊢ (𝜑 ↔ (⊤ ∧ 𝜓))

Proof of Theorem tradd

Step	Hyp	Ref	Expression
1		tradd.1	. 2 ⊢ (𝜑 ↔ 𝜓)
2		truan 1550	. 2 ⊢ ((⊤ ∧ 𝜓) ↔ 𝜓)
3	1, 2	bitr4i 277	1 ⊢ (𝜑 ↔ (⊤ ∧ 𝜓))

Syntax hints:   ↔ wb 205   ∧ wa 395  ⊤wtru 1540

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 206  df-an 396  df-tru 1542

This theorem is referenced by: (None)