Theorem bnj564

Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011) (New usage is discouraged.)

	Ref	Expression
Hypothesis	bnj564.17	⊢ ( 𝜏 ↔ ( 𝑓 Fn 𝑚 ∧ 𝜑′ ∧ 𝜓′ ) )
Assertion	bnj564	⊢ ( 𝜏 → dom 𝑓 = 𝑚 )

Proof

Step	Hyp	Ref	Expression
1		bnj564.17	⊢ ( 𝜏 ↔ ( 𝑓 Fn 𝑚 ∧ 𝜑′ ∧ 𝜓′ ) )
2	1	simp1bi	⊢ ( 𝜏 → 𝑓 Fn 𝑚 )
3	2	fndmd	⊢ ( 𝜏 → dom 𝑓 = 𝑚 )