Theorem bnj937 32043

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 220	1 ⊢ (𝜑 → 𝜓)

Syntax hints:   → wi 4  ∃wex 1780

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1911  ax-6 1970

This theorem depends on definitions:  df-bi 209  df-ex 1781

This theorem is referenced by:  bnj1265  32084  bnj1379  32102  bnj852  32193  bnj1148  32268  bnj1154  32271  bnj1189  32281  bnj1245  32286  bnj1286  32291  bnj1311  32296  bnj1371  32301  bnj1374  32303  bnj1498  32333  bnj1514  32335