Theorem bnj101 31309

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

Hypotheses

Ref	Expression
bnj101.1	⊢ ∃𝑥𝜑
bnj101.2	⊢ (𝜑 → 𝜓)

Assertion

Ref	Expression
bnj101	⊢ ∃𝑥𝜓

Proof of Theorem bnj101

Step	Hyp	Ref	Expression
1		bnj101.1	. 2 ⊢ ∃𝑥𝜑
2		bnj101.2	. 2 ⊢ (𝜑 → 𝜓)
3	1, 2	eximii 1932	1 ⊢ ∃𝑥𝜓

Syntax hints:   → wi 4  ∃wex 1875

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1891  ax-4 1905

This theorem depends on definitions:  df-bi 199  df-ex 1876

This theorem is referenced by:  bnj1023  31368  bnj1098  31371  bnj1101  31372  bnj1109  31374  bnj1468  31433  bnj907  31552  bnj1110  31567  bnj1118  31569  bnj1128  31575  bnj1145  31578  bnj1172  31586  bnj1174  31588  bnj1176  31590