Theorem alloverimex-P5.RC.GEN 603

Description: Inference Form of alloverimex-P5 601 with Generalization.

For the deductive form with a variable restriction, see alloverimex-P5.GENV 622. For the most general form see alloverimex-P5.GENF 748.

Hypothesis

Ref	Expression
alloverimex-P5.RC.GEN.1	⊢ (𝜑 → 𝜓)

Assertion

Ref	Expression
alloverimex-P5.RC.GEN	⊢ (∃𝑥𝜑 → ∃𝑥𝜓)

Proof of Theorem alloverimex-P5.RC.GEN

Step	Hyp	Ref	Expression
1		alloverimex-P5.RC.GEN.1	. . 3 ⊢ (𝜑 → 𝜓)
2	1	ax-GEN 15	. 2 ⊢ ∀𝑥(𝜑 → 𝜓)
3	2	alloverimex-P5.RC 602	1 ⊢ (∃𝑥𝜑 → ∃𝑥𝜓)

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

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:  subexinf-P5  608  qimeqex-P5-L1  610  exiav-P5  615  gennfrw-P6  685  nfrex2w-P6  695  trnsvsubw-P6  710  gennfr-P6  734  nfrex2-P6  744  exia-P6  746  trnsvsub-P6  763  lemma-L6.07a-L1  770  lemma-L6.07a-L2  771