Theorem tradd 38782

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 1581	. 2 ⊢ ((⊤ ∧ 𝜓) ↔ 𝜓)
3	1, 2	bitr4i 281	1 ⊢ (𝜑 ↔ (⊤ ∧ 𝜓))

This proof depends on syntax axioms:   ↔ wb 209   ∧ wa 400  ⊤wtru 1571

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 210  df-an 401  df-tru 1573

This theorem is used by: (None)