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Metamath Proof Explorer

Theorem bnj561

Description: Technical lemma for bnj852 . This lemma may no longer be used or have become an indirect lemma of the theorem in question (i.e. a lemma of a lemma... of the theorem). (Contributed by Jonathan Ben-Naim, 3-Jun-2011) (New usage is discouraged.)

	Ref	Expression
Hypotheses	bnj561.18	$⊢ σ \leftrightarrow (m \in D \land n = suc m \land p \in m)$
	bnj561.19	$⊢ η \leftrightarrow (m \in D \land n = suc m \land p \in ω \land m = suc p)$
	bnj561.37	$⊢ (R FrSe A \land τ \land σ) \to G Fn n$
Assertion	bnj561	$⊢ (R FrSe A \land τ \land η) \to G Fn n$

Proof

Step	Hyp	Ref	Expression
1		bnj561.18	$⊢ σ \leftrightarrow (m \in D \land n = suc m \land p \in m)$
2		bnj561.19	$⊢ η \leftrightarrow (m \in D \land n = suc m \land p \in ω \land m = suc p)$
3		bnj561.37	$⊢ (R FrSe A \land τ \land σ) \to G Fn n$
4	1 2	bnj556	$⊢ η \to σ$
5	4 3	syl3an3	$⊢ (R FrSe A \land τ \land η) \to G Fn n$