Theorem bnj101 35021

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 1859	1 ⊢ ∃𝑥𝜓

Syntax hints:   → wi 4  ∃wex 1801

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1817  ax-4 1831

This theorem depends on definitions:  df-bi 209  df-ex 1802

This theorem is referenced by:  bnj1023  35078  bnj1098  35081  bnj1101  35082  bnj1109  35084  bnj1468  35143  bnj907  35264  bnj1110  35279  bnj1118  35281  bnj1128  35287  bnj1145  35290  bnj1172  35298  bnj1174  35300  bnj1176  35302