Theorem bnj937 31387

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 2086	. 2 ⊢ (∃𝑥𝜓 ↔ 𝜓)
3	1, 2	sylib 210	1 ⊢ (𝜑 → 𝜓)

Syntax hints:   → wi 4  ∃wex 1880

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1896  ax-4 1910  ax-5 2011  ax-6 2077

This theorem depends on definitions:  df-bi 199  df-ex 1881

This theorem is referenced by:  bnj1265  31428  bnj1379  31446  bnj852  31536  bnj1148  31609  bnj1154  31612  bnj1189  31622  bnj1245  31627  bnj1286  31632  bnj1311  31637  bnj1371  31642  bnj1374  31644  bnj1498  31674  bnj1514  31676