Theorem bnj101 35220

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 1870	1 ⊢ ∃𝑥𝜓

This proof depends on syntax axioms:   → wi 4  ∃wex 1812

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1828  ax-4 1842

This proof depends on definitions:  df-bi 210  df-ex 1813

This theorem is used by:  bnj1023  35277  bnj1098  35280  bnj1101  35281  bnj1109  35283  bnj1468  35342  bnj907  35463  bnj1110  35478  bnj1118  35480  bnj1128  35486  bnj1145  35489  bnj1172  35497  bnj1174  35499  bnj1176  35501