Theorem bnj101 31988

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 1833	1 ⊢ ∃𝑥𝜓

Syntax hints:   → wi 4  ∃wex 1776

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806

This theorem depends on definitions:  df-bi 209  df-ex 1777

This theorem is referenced by:  bnj1023  32047  bnj1098  32050  bnj1101  32051  bnj1109  32053  bnj1468  32113  bnj907  32234  bnj1110  32249  bnj1118  32251  bnj1128  32257  bnj1145  32260  bnj1172  32268  bnj1174  32270  bnj1176  32272