Theorem bnj101 32602

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 1840	1 ⊢ ∃𝑥𝜓

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

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

This theorem is referenced by:  bnj1023  32660  bnj1098  32663  bnj1101  32664  bnj1109  32666  bnj1468  32726  bnj907  32847  bnj1110  32862  bnj1118  32864  bnj1128  32870  bnj1145  32873  bnj1172  32881  bnj1174  32883  bnj1176  32885