Theorem exiav-P5.SH 616

Description: Inference Form of exiav-P5 615.

Hypotheses

Ref	Expression
exiav-P5.SH.1	⊢ (𝜑 → 𝜓)
exiav-P5.SH.2	⊢ ∃𝑥𝜑

Assertion

Ref	Expression
exiav-P5.SH	⊢ 𝜓

Distinct variable group:   𝜓,𝑥

Proof of Theorem exiav-P5.SH

Step	Hyp	Ref	Expression
1		exiav-P5.SH.2	. 2 ⊢ ∃𝑥𝜑
2		exiav-P5.SH.1	. . 3 ⊢ (𝜑 → 𝜓)
3	2	exiav-P5 615	. 2 ⊢ (∃𝑥𝜑 → 𝜓)
4	1, 3	rcp-NDIME0 228	1 ⊢ 𝜓

Syntax hints:   → wff-imp 10  ∃wff-exists 595

This theorem was proved from axioms:  ax-L1 11  ax-L2 12  ax-L3 13  ax-MP 14  ax-GEN 15  ax-L4 16  ax-L5 17

This theorem depends on definitions:  df-bi-D2.1 107  df-and-D2.2 133  df-or-D2.3 145  df-true-D2.4 155  df-rcp-AND3 161  df-exists-D5.1 596

This theorem is referenced by:  eqref-P5  626  exi-P6  718  nfrsucc-P6  780  nfradd-P6  781  nfrmult-P6  782  psubsuccv-P6-L1  805  psubaddv-P6-L1  807  psubmultv-P6-L1  809