Theorem bnj101 34737

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 1837	1 ⊢ ∃𝑥𝜓

Syntax hints:   → wi 4  ∃wex 1779

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809

This theorem depends on definitions:  df-bi 207  df-ex 1780

This theorem is referenced by:  bnj1023  34794  bnj1098  34797  bnj1101  34798  bnj1109  34800  bnj1468  34860  bnj907  34981  bnj1110  34996  bnj1118  34998  bnj1128  35004  bnj1145  35007  bnj1172  35015  bnj1174  35017  bnj1176  35019