Theorem trueie-P4.22a 444

Description: '⊤' Introduction and Elimination (closed form). †

Assertion

Ref	Expression
trueie-P4.22a	⊢ ((⊤ → 𝜑) ↔ 𝜑)

Proof of Theorem trueie-P4.22a

Step	Hyp	Ref	Expression
1		ndime-P3.6.CL 244	. . . 4 ⊢ ((⊤ ∧ (⊤ → 𝜑)) → 𝜑)
2	1	rcp-NDIMI2 224	. . 3 ⊢ (⊤ → ((⊤ → 𝜑) → 𝜑))
3	2	ndtruee-P3.18 183	. 2 ⊢ ((⊤ → 𝜑) → 𝜑)
4		axL1-P3.21.CL 253	. 2 ⊢ (𝜑 → (⊤ → 𝜑))
5	3, 4	rcp-NDBII0 239	1 ⊢ ((⊤ → 𝜑) ↔ 𝜑)

Syntax hints:   → wff-imp 10   ↔ wff-bi 104  ⊤wff-true 153

This theorem was proved from axioms:  ax-L1 11  ax-L2 12  ax-L3 13  ax-MP 14

This theorem depends on definitions:  df-bi-D2.1 107  df-and-D2.2 133  df-true-D2.4 155

This theorem is referenced by:  oroverim-P4.28-L1  465  truthtbltimt-P4.36a  495  truthtbltimf-P4.36b  496  solvesub-P6a  704  lemma-L6.02a  726  psubnfr-P6  784