Theorem bnj101 32103

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 1838	1 ⊢ ∃𝑥𝜓

Syntax hints:   → wi 4  ∃wex 1781

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811

This theorem depends on definitions:  df-bi 210  df-ex 1782

This theorem is referenced by:  bnj1023  32162  bnj1098  32165  bnj1101  32166  bnj1109  32168  bnj1468  32228  bnj907  32349  bnj1110  32364  bnj1118  32366  bnj1128  32372  bnj1145  32375  bnj1172  32383  bnj1174  32385  bnj1176  32387