Theorem eximii 1648

Description: Inference associated with eximi 1646. (Contributed by BJ, 3-Feb-2018.)

Hypotheses

Ref	Expression
eximii.1	⊢ ∃𝑥𝜑
eximii.2	⊢ (𝜑 → 𝜓)

Assertion

Ref	Expression
eximii	⊢ ∃𝑥𝜓

Proof of Theorem eximii

Step	Hyp	Ref	Expression
1		eximii.1	. 2 ⊢ ∃𝑥𝜑
2		eximii.2	. . 3 ⊢ (𝜑 → 𝜓)
3	2	eximi 1646	. 2 ⊢ (∃𝑥𝜑 → ∃𝑥𝜓)
4	1, 3	ax-mp 5	1 ⊢ ∃𝑥𝜓

Syntax hints:   → wi 4  ∃wex 1538

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1493  ax-gen 1495  ax-ie1 1539  ax-ie2 1540  ax-4 1556  ax-ial 1580

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  spimfv  1745  ax6evr  1751  spimed  1786  darii  2178  barbari  2180  festino  2184  baroco  2185  cesaro  2186  camestros  2187  datisi  2188  disamis  2189  felapton  2192  darapti  2193  dimatis  2195  fresison  2196  calemos  2197  fesapo  2198  bamalip  2199  ceqsexv2d  2840  vtoclf  2854  vtocl2  2856  vtocl3  2857  nalset  4213  el  4261  dtruarb  4274  snnex  4538  eusv2nf  4546  dtruex  4650  limom  4705  nninfct  12557  bj-axemptylem  16213  bj-nalset  16216  bj-d0clsepcl  16246  bj-omex2  16298  bj-nn0sucALT  16299