Theorem aistbistaandb 46864

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.)

Hypotheses

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

Assertion

Ref	Expression
aistbistaandb	⊢ (𝜑 ∧ 𝜓)

Proof of Theorem aistbistaandb

Step	Hyp	Ref	Expression
1		aistbistaandb.1	. . 3 ⊢ (𝜑 ↔ ⊤)
2	1	aistia 46851	. 2 ⊢ 𝜑
3		aistbistaandb.2	. . 3 ⊢ (𝜓 ↔ ⊤)
4	3	aistia 46851	. 2 ⊢ 𝜓
5	2, 4	pm3.2i 470	1 ⊢ (𝜑 ∧ 𝜓)

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)