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Metamath Proof Explorer

Theorem bnj132

Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011) (Proof shortened by Andrew Salmon, 26-Jun-2011) (New usage is discouraged.)

		Ref	Expression
	Hypothesis	bnj132.1	⊢ ( 𝜑 ↔ ∃ 𝑥 ( 𝜓 → 𝜒 ) )
	Assertion	bnj132	⊢ ( 𝜑 ↔ ( 𝜓 → ∃ 𝑥 𝜒 ) )

Proof

Step	Hyp	Ref	Expression
1		bnj132.1	⊢ ( 𝜑 ↔ ∃ 𝑥 ( 𝜓 → 𝜒 ) )
2		19.37v	⊢ ( ∃ 𝑥 ( 𝜓 → 𝜒 ) ↔ ( 𝜓 → ∃ 𝑥 𝜒 ) )
3	1 2	bitri	⊢ ( 𝜑 ↔ ( 𝜓 → ∃ 𝑥 𝜒 ) )