Theorem bnj937 30842

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

Hypothesis

Ref	Expression
bnj937.1	⊢ (𝜑 → ∃𝑥𝜓)

Assertion

Ref	Expression
bnj937	⊢ (𝜑 → 𝜓)

Distinct variable group:   𝜓,𝑥

Allowed substitution hint:   𝜑(𝑥)

Proof of Theorem bnj937

Step	Hyp	Ref	Expression
1		bnj937.1	. 2 ⊢ (𝜑 → ∃𝑥𝜓)
2		19.9v 1896	. 2 ⊢ (∃𝑥𝜓 ↔ 𝜓)
3	1, 2	sylib 208	1 ⊢ (𝜑 → 𝜓)

Syntax hints:   → wi 4  ∃wex 1704

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888

This theorem depends on definitions:  df-bi 197  df-ex 1705

This theorem is referenced by:  bnj1265  30883  bnj1379  30901  bnj852  30991  bnj1148  31064  bnj1154  31067  bnj1189  31077  bnj1245  31082  bnj1286  31087  bnj1311  31092  bnj1371  31097  bnj1374  31099  bnj1498  31129  bnj1514  31131