Theorem eximii 1613

Description: Inference associated with eximi 1611. (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 1611	. 2 ⊢ (∃𝑥𝜑 → ∃𝑥𝜓)
4	1, 3	ax-mp 5	1 ⊢ ∃𝑥𝜓

Syntax hints:   → wi 4  ∃wex 1503

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 1458  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-4 1521  ax-ial 1545

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  spimfv  1710  ax6evr  1716  spimed  1751  darii  2142  barbari  2144  festino  2148  baroco  2149  cesaro  2150  camestros  2151  datisi  2152  disamis  2153  felapton  2156  darapti  2157  dimatis  2159  fresison  2160  calemos  2161  fesapo  2162  bamalip  2163  vtoclf  2813  vtocl2  2815  vtocl3  2816  nalset  4159  el  4207  dtruarb  4220  snnex  4479  eusv2nf  4487  dtruex  4591  limom  4646  nninfct  12178  bj-axemptylem  15384  bj-nalset  15387  bj-d0clsepcl  15417  bj-omex2  15469  bj-nn0sucALT  15470