Theorem tradd 38129

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 1551	. 2 ⊢ ((⊤ ∧ 𝜓) ↔ 𝜓)
3	1, 2	bitr4i 278	1 ⊢ (𝜑 ↔ (⊤ ∧ 𝜓))

Syntax hints:   ↔ wb 206   ∧ wa 395  ⊤wtru 1541

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 207  df-an 396  df-tru 1543

This theorem is referenced by: (None)