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Metamath Proof Explorer

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	\|- ( T. -> ph )
	Assertion	mptru	\|- ph

Proof

Step	Hyp	Ref	Expression
1		mptru.1	\|- ( T. -> ph )
2		tru	\|- T.
3	2 1	ax-mp	\|- ph