Theorem bnj937 32651

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 1988	. 2 ⊢ (∃𝑥𝜓 ↔ 𝜓)
3	1, 2	sylib 217	1 ⊢ (𝜑 → 𝜓)

Syntax hints:   → wi 4  ∃wex 1783

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1799  ax-4 1813  ax-5 1914  ax-6 1972

This theorem depends on definitions:  df-bi 206  df-ex 1784

This theorem is referenced by:  bnj1265  32692  bnj1379  32710  bnj852  32801  bnj1148  32876  bnj1154  32879  bnj1189  32889  bnj1245  32894  bnj1286  32899  bnj1311  32904  bnj1371  32909  bnj1374  32911  bnj1498  32941  bnj1514  32943