Theorem bnj101 30043

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 1754	1 ⊢ ∃𝑥𝜓

Syntax hints:   → wi 4  ∃wex 1695

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728

This theorem depends on definitions:  df-bi 196  df-ex 1696

This theorem is referenced by:  bnj1023  30105  bnj1098  30108  bnj1101  30109  bnj1109  30111  bnj1468  30170  bnj907  30289  bnj1110  30304  bnj1118  30306  bnj1128  30312  bnj1145  30315  bnj1172  30323  bnj1174  30325  bnj1176  30327