Theorem bnj1239 32072

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

Assertion

Ref	Expression
bnj1239	⊢ (∃𝑥 ∈ 𝐴 (𝜓 ∧ 𝜒) → ∃𝑥 ∈ 𝐴 𝜓)

Proof of Theorem bnj1239

Step	Hyp	Ref	Expression
1		simpl 485	. 2 ⊢ ((𝜓 ∧ 𝜒) → 𝜓)
2	1	reximi 3243	1 ⊢ (∃𝑥 ∈ 𝐴 (𝜓 ∧ 𝜒) → ∃𝑥 ∈ 𝐴 𝜓)

Syntax hints:   → wi 4   ∧ wa 398  ∃wrex 3139

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806

This theorem depends on definitions:  df-bi 209  df-an 399  df-ex 1777  df-ral 3143  df-rex 3144

This theorem is referenced by:  bnj1238  32073  bnj1299  32085  bnj66  32127