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Metamath Proof Explorer

Theorem ex-natded5.3i

Description: The same as ex-natded5.3 and ex-natded5.3-2 but with no context. Identical to jccir , which should be used instead. (Contributed by Mario Carneiro, 9-Feb-2017) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	ex-natded5.3i.1	⊢ ( 𝜓 → 𝜒 )
	ex-natded5.3i.2	⊢ ( 𝜒 → 𝜃 )
Assertion	ex-natded5.3i	⊢ ( 𝜓 → ( 𝜒 ∧ 𝜃 ) )

Proof

Step	Hyp	Ref	Expression
1		ex-natded5.3i.1	⊢ ( 𝜓 → 𝜒 )
2		ex-natded5.3i.2	⊢ ( 𝜒 → 𝜃 )
3	1 2	syl	⊢ ( 𝜓 → 𝜃 )
4	1 3	jca	⊢ ( 𝜓 → ( 𝜒 ∧ 𝜃 ) )