Theorem bnj1299 32083

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

Hypothesis

Ref	Expression
bnj1299.1	⊢ (𝜑 → ∃𝑥 ∈ 𝐴 (𝜓 ∧ 𝜒))

Assertion

Ref	Expression
bnj1299	⊢ (𝜑 → ∃𝑥 ∈ 𝐴 𝜓)

Proof of Theorem bnj1299

Step	Hyp	Ref	Expression
1		bnj1299.1	. 2 ⊢ (𝜑 → ∃𝑥 ∈ 𝐴 (𝜓 ∧ 𝜒))
2		bnj1239 32070	. 2 ⊢ (∃𝑥 ∈ 𝐴 (𝜓 ∧ 𝜒) → ∃𝑥 ∈ 𝐴 𝜓)
3	1, 2	syl 17	1 ⊢ (𝜑 → ∃𝑥 ∈ 𝐴 𝜓)

Syntax hints:   → wi 4   ∧ wa 398  ∃wrex 3137

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1790  ax-4 1804

This theorem depends on definitions:  df-bi 209  df-an 399  df-ex 1775  df-ral 3141  df-rex 3142

This theorem is referenced by:  bnj1497  32325  bnj1498  32326  bnj1501  32332