Theorem rcp-NDBIER0 241

Description: '↔' Elimination by Reverse Implication Introduction. †

Hypothesis

Ref	Expression
rcp-NDBIER0.1	⊢ (𝜑 ↔ 𝜓)

Assertion

Ref	Expression
rcp-NDBIER0	⊢ (𝜓 → 𝜑)

Proof of Theorem rcp-NDBIER0

Step	Hyp	Ref	Expression
1		rcp-NDBIER0.1	. . . 4 ⊢ (𝜑 ↔ 𝜓)
2	1	ndtruei-P3.17 182	. . 3 ⊢ (⊤ → (𝜑 ↔ 𝜓))
3	2	ndbier-P3.15 180	. 2 ⊢ (⊤ → (𝜓 → 𝜑))
4	3	ndtruee-P3.18 183	1 ⊢ (𝜓 → 𝜑)

Syntax hints:   → wff-imp 10   ↔ 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:  idandthml-P4.23a  446  idandthmr-P4.23b  447  idornthml-P4.24a  448  idornthmr-P4.24b  449  oroverim-P4.28-L1  465  suballinf-P5  594  subexinf-P5  608  ndnfrneg-P7.2  827  lemma-L7.02a  944  dfexistsint-P7  960  cbvex-P7-L1  1065  nfrnegconv-P8  1110