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Metamath Proof Explorer

Theorem trunanfal

Description: A -/\ identity. (Contributed by Anthony Hart, 23-Oct-2010) (Proof shortened by Andrew Salmon, 13-May-2011) (Proof shortened by Wolf Lammen, 10-Jul-2020)

		Ref	Expression
	Assertion	trunanfal	⊢ ( ( ⊤ ⊼ ⊥ ) ↔ ⊤ )

Proof

Step	Hyp	Ref	Expression
1		df-nan	⊢ ( ( ⊤ ⊼ ⊥ ) ↔ ¬ ( ⊤ ∧ ⊥ ) )
2		truanfal	⊢ ( ( ⊤ ∧ ⊥ ) ↔ ⊥ )
3	1 2	xchbinx	⊢ ( ( ⊤ ⊼ ⊥ ) ↔ ¬ ⊥ )
4		notfal	⊢ ( ¬ ⊥ ↔ ⊤ )
5	3 4	bitri	⊢ ( ( ⊤ ⊼ ⊥ ) ↔ ⊤ )