Theorem bnj937 32747

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 1991	. 2 ⊢ (∃𝑥𝜓 ↔ 𝜓)
3	1, 2	sylib 217	1 ⊢ (𝜑 → 𝜓)

Syntax hints:   → wi 4  ∃wex 1786

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1802  ax-4 1816  ax-5 1917  ax-6 1975

This theorem depends on definitions:  df-bi 206  df-ex 1787

This theorem is referenced by:  bnj1265  32788  bnj1379  32806  bnj852  32897  bnj1148  32972  bnj1154  32975  bnj1189  32985  bnj1245  32990  bnj1286  32995  bnj1311  33000  bnj1371  33005  bnj1374  33007  bnj1498  33037  bnj1514  33039