Theorem bnj1266 35208

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

Hypothesis

Ref	Expression
bnj1266.1	⊢ (𝜒 → ∃𝑥(𝜑 ∧ 𝜓))

Assertion

Ref	Expression
bnj1266	⊢ (𝜒 → ∃𝑥𝜓)

Proof of Theorem bnj1266

Step	Hyp	Ref	Expression
1		bnj1266.1	. 2 ⊢ (𝜒 → ∃𝑥(𝜑 ∧ 𝜓))
2		simpr 489	. 2 ⊢ ((𝜑 ∧ 𝜓) → 𝜓)
3	1, 2	bnj593 35143	1 ⊢ (𝜒 → ∃𝑥𝜓)

This proof depends on syntax axioms:   → wi 4   ∧ wa 400  ∃wex 1808

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1824  ax-4 1838

This proof depends on definitions:  df-bi 210  df-an 401  df-ex 1809

This theorem is used by:  bnj1265  35209