Theorem bnj101 35354

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 1869	1 ⊢ ∃𝑥𝜓

This proof depends on syntax axioms:   → wi 4  ∃wex 1811

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1827  ax-4 1841

This proof depends on definitions:  df-bi 210  df-ex 1812

This theorem is used by:  bnj1023  35411  bnj1098  35414  bnj1101  35415  bnj1109  35417  bnj1468  35476  bnj907  35597  bnj1110  35612  bnj1118  35614  bnj1128  35620  bnj1145  35623  bnj1172  35631  bnj1174  35633  bnj1176  35635