Theorem bimpf-P4.RC 532

Description: Inference Form of bimpf-P4 531. †

Hypotheses

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

Assertion

Ref	Expression
bimpf-P4.RC	⊢ 𝜓

Proof of Theorem bimpf-P4.RC

Step	Hyp	Ref	Expression
1		bimpf-P4.RC.1	. . . 4 ⊢ 𝜑
2	1	ndtruei-P3.17 182	. . 3 ⊢ (⊤ → 𝜑)
3		bimpf-P4.RC.2	. . . 4 ⊢ (𝜑 ↔ 𝜓)
4	3	ndtruei-P3.17 182	. . 3 ⊢ (⊤ → (𝜑 ↔ 𝜓))
5	2, 4	bimpf-P4 531	. 2 ⊢ (⊤ → 𝜓)
6	5	ndtruee-P3.18 183	1 ⊢ 𝜓

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:  example-E5.04a  675  nfrgenw-P6  684  nfrim-P6  689  nfrex2w-P6  695  exgennfrw-P6  697  qimeqalla-P6-L1  698  qimeqallb-P6-L1  700  solvesub-P6a  704  example-E6.01a  706  example-E6.02a  712  qremall-P6  722  qremex-P6  723  lemma-L6.02a  726  genex-P6  731  nfrgen-P6  733  exgennfr-P6  736  genall-P6  737  nfrterm-P6  779  psubsuccv-P6  806  psubaddv-P6  808  psubmultv-P6  810  ndexe-P6  825  axL12-P7  982  gennfr-P8  1079  exgennfr-P8  1085  nfrsucc-P8  1119  nfradd-P8  1120  nfrmult-P8  1121