Theorem ndnfrleq-P7.11.RC 882

Description: Inference Form of ndnfrleq-P7.11 836. †

Hypothesis

Ref	Expression
ndnfrleq-P7.11.RC.1	⊢ (𝜑 ↔ 𝜓)

Assertion

Ref	Expression
ndnfrleq-P7.11.RC	⊢ (Ⅎ𝑥𝜑 ↔ Ⅎ𝑥𝜓)

Proof of Theorem ndnfrleq-P7.11.RC

Step	Hyp	Ref	Expression
1		ndnfrleq-P7.11.RC.1	. . . 4 ⊢ (𝜑 ↔ 𝜓)
2	1	ndtruei-P3.17 182	. . 3 ⊢ (⊤ → (𝜑 ↔ 𝜓))
3	2	ndnfrleq-P7.11.VR 862	. 2 ⊢ (⊤ → (Ⅎ𝑥𝜑 ↔ Ⅎ𝑥𝜓))
4	3	ndtruee-P3.18 183	1 ⊢ (Ⅎ𝑥𝜑 ↔ Ⅎ𝑥𝜓)

Syntax hints:   ↔ wff-bi 104  ⊤wff-true 153  Ⅎwff-nfree 681

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  ax-L6 18  ax-L7 19  ax-L12 29

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  df-nfree-D6.1 682

This theorem is referenced by:  nfrthm-P7  926  gennfr-P8  1079  exgennfr-P8  1085