Theorem bimpr-P4.RC 534

Description: Inference Form of bimpr-P4 533. †

Hypotheses

Ref	Expression
bimpr-P4.RC.1	⊢ 𝜓
bimpr-P4.RC.2	⊢ (𝜑 ↔ 𝜓)

Assertion

Ref	Expression
bimpr-P4.RC	⊢ 𝜑

Proof of Theorem bimpr-P4.RC

Step	Hyp	Ref	Expression
1		bimpr-P4.RC.1	. . . 4 ⊢ 𝜓
2	1	ndtruei-P3.17 182	. . 3 ⊢ (⊤ → 𝜓)
3		bimpr-P4.RC.2	. . . 4 ⊢ (𝜑 ↔ 𝜓)
4	3	ndtruei-P3.17 182	. . 3 ⊢ (⊤ → (𝜑 ↔ 𝜓))
5	2, 4	bimpr-P4 533	. 2 ⊢ (⊤ → 𝜑)
6	5	ndtruee-P3.18 183	1 ⊢ 𝜑

Syntax hints:   ↔ wff-bi 104  ⊤wff-true 153

This theorem was proved from axioms:  ax-L1 11  ax-L2 12  ax-L3 13  ax-MP 14

This theorem depends on definitions:  df-bi-D2.1 107  df-true-D2.4 155

This theorem is referenced by:  axL5ex-P5  613  axL6ex-P5  625  exgenallw-P6  680  gennfrw-P6  685  nfrim-P6  689  nfrand-P6  690  nfrbi-P6  691  nfrex2w-P6  695  nfrexgenw-P6  696  exi-P6  718  exgenall-P6  732  gennfr-P6  734  nfrexgen-P6  735  cbvex-P6  752  qcexandl-P6  762  lemma-L6.06a  766  psubthm-P6  786  nfrnfr-P6  821  axL6ex-P7  925  nfrthm-P7  926  nfrzero-P8  1117  nfrvar-P8  1118  nfrsucc-P8  1119  nfradd-P8  1120  nfrmult-P8  1121