Theorem truconj 38049

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 1550	. 2 ⊢ ((⊤ ∧ 𝜑) ↔ 𝜑)
2	1	bicomi 224	1 ⊢ (𝜑 ↔ (⊤ ∧ 𝜑))

Syntax hints:   ↔ wb 206   ∧ 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 207  df-an 396  df-tru 1542

This theorem is referenced by: (None)