Theorem astbstanbst

Description: Given a is equivalent to T., also given that b is equivalent to T, there exists a proof for a and b is equivalent to T. (Contributed by Jarvin Udandy, 29-Aug-2016)

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

Proof

Step	Hyp	Ref	Expression
1		astbstanbst.1	⊢ ( 𝜑 ↔ ⊤ )
2		astbstanbst.2	⊢ ( 𝜓 ↔ ⊤ )
3	1	aistia	⊢ 𝜑
4	2	aistia	⊢ 𝜓
5	3 4	pm3.2i	⊢ ( 𝜑 ∧ 𝜓 )
6	5	bitru	⊢ ( ( 𝜑 ∧ 𝜓 ) ↔ ⊤ )