Theorem mptru

Description: Eliminate T. as an antecedent. A proposition implied by T. is true. This is modus ponens ax-mp when the minor hypothesis is T. (which holds by tru ). (Contributed by Mario Carneiro, 13-Mar-2014)

	Ref	Expression
Hypothesis	mptru.1	⊢ ( ⊤ → 𝜑 )
Assertion	mptru	⊢ 𝜑

Proof

Step	Hyp	Ref	Expression
1		mptru.1	⊢ ( ⊤ → 𝜑 )
2		tru	⊢ ⊤
3	2 1	ax-mp	⊢ 𝜑