Theorem aistbistaandb

Description: Given a is equivalent to T., also given that b is equivalent to T, there exists a proof for (a and b). (Contributed by Jarvin Udandy, 9-Sep-2016)

	Ref	Expression
Hypotheses	aistbistaandb.1	⊢ ( 𝜑 ↔ ⊤ )
	aistbistaandb.2	⊢ ( 𝜓 ↔ ⊤ )
Assertion	aistbistaandb	⊢ ( 𝜑 ∧ 𝜓 )

Proof

Step	Hyp	Ref	Expression
1		aistbistaandb.1	⊢ ( 𝜑 ↔ ⊤ )
2		aistbistaandb.2	⊢ ( 𝜓 ↔ ⊤ )
3	1	aistia	⊢ 𝜑
4	2	aistia	⊢ 𝜓
5	3 4	pm3.2i	⊢ ( 𝜑 ∧ 𝜓 )