Theorem truconj 38778

Description: Add true as a conjunct. (Contributed by Giovanni Mascellani, 23-May-2019.)

Assertion

Ref	Expression
truconj	⊢ (𝜑 ↔ (⊤ ∧ 𝜑))

Proof of Theorem truconj

Step	Hyp	Ref	Expression
1		truan 1581	. 2 ⊢ ((⊤ ∧ 𝜑) ↔ 𝜑)
2	1	bicomi 227	1 ⊢ (𝜑 ↔ (⊤ ∧ 𝜑))

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)